[math]\begin{cases} \text-4x+3y=23 \\ x-y=\text-7 \\ \end{cases}[/math]
[math]\begin{cases} 6x-5y=34 \\ 3x+2y=8 \\ \end{cases}[/math][br][br][size=150]She starts by rearranging the second equation to isolate the [math]y[/math] variable: [math]y=4-1.5x[/math]. [br]She then substituted the expression [math]4-1.5x[/math] for [math]y[/math] in the first equation, as shown: [/size][br][br][math]\begin{align} 6x-5(4-1.5x) &= 34 \\ 6x-20-7.5x &= 34 \\ \text-1.5x &= 54 \\ x &= \text-36 \\ \end{align}[/math][br][math]\begin{align}y&=4-1.5x\\y &= 4-1.5 \cdot (\text-36) \\ y &= 58 \\ \end{align}[/math][br][br]Check to see if Lin's solution of [math]\left(-36,58\right)[/math] makes both equations in the system true.
If your answer to the previous question is "no," find and explain her mistake. If your answer is "yes," graph the equations to verify the solution of the system.[br]
[math]\begin{cases} 2x-4y=20\\ x=4 \\ \end{cases}[/math]
[math]\begin{cases} y=6x+11 \\ 2x-3y=7 \\ \end{cases}[/math]
[math]\begin{cases} x+3y=\text-5\\ 9x+3y=3 \end{cases}[/math][br][br][size=150]Tyler's first step is to isolate [math]x[/math] in the first equation to get [math]x=-5-3y[/math]. [br]Han's first step is to isolate [math]3y[/math] in the first equation to get [math]3y=-5-x[/math].[br][/size][br]Show that both first steps can be used to solve the system and will yield the same solution.
[table][tr][td][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdcAAACFCAYAAAAJtbKJAAAfVklEQVR4Ae2de+wdRRXHa4zREESiNUYitGrLo6KA8jBYBSIQMAEbVJBApUFJAGuKf/hIACmCWpJKq1CNQkGqYAJC0RIiSrHxQVKM8tKCQaD8IxgeFUqMKGHM5ybnx/nNnb33/l7tztnvJDezO3vmzPl+z8yc3dm9u7OSkhgQA2JADIgBMTCtDMyaVm1SJgbEgBgQA2JADCQFV3UCMdBiBp566ql0yimnpDe84Q1pzpw5acWKFS22VqaJATFgDCi4GhPKxUALGTjmmGPSrFmzxv2uvvrqFloqk8SAGPAMKLh6NrQtBlrEwNatW8cFVQuyxx9/fIuslCliQAyUGFBwLbGiMjHQAgaeeOIJBdcW+EEmiIHJMKDgOhnWVEcM7CAGjjvuuL4Ae8011+yg1tWMGBADk2VAwXWyzKmeGNgBDDz99NPp9NNPT2984xvTvHnz0sqVK3dAq2pCDIiBqTKg4DpVBlVfDIgBMSAGxEDGgIJrRoh2xYAYEANiQAxMlQEF16kyqPpiQAyIATEgBjIGFFwzQrQrBtrGwOrVqxMPNi1evDht3LixbeZNiz3r169PJ598cjrxxBPT2rVrp0WnlIiBncmAguvOZF9ti4EhDJx99tl9Twv/+te/HlKrrsPr1q3rw7h8+fK6QMhaMZAxoOCaEaJdMdAWBp599tm+oMOLJD796U+3xcRpseNDH/pQH87Zs2dPi24pEQM7iwEF153FvNoVA0MYeOihh/qCDsF14cKFQ2rWdZh3Jtvbp3y+ffv2uoDIWjHgGFBwdWRoUwy0jYH99tuvL/BccsklbTNzSvaUlr6PPvroKelUZTGwsxlQcN3ZHlD7YmAAA3fddVd697vfPRZg+UJOtPT888+nY489dgzjQQcdlB588MFoMIWnYwwouHbM4YJbJwN//OMf06OPPlqn8SNazTL4fffdN6K0xMRAuxlQcG23f2SdGBADYkAMVMiAgmuFTpPJYkAMiAEx0G4GFFzb7R9ZN4SBDRs2JP4TecsttwyRrPcwS8KXXXZZ4iPpL774Yr1ABlj+5JNPpjVr1qTLL788bdmyZYCkDomBOhhQcK3DT7KywMBpp5029hAMf+Hg7T7R0qpVq8ZhnDt3bnrsscdCwbz77rvTbrvtNg7nDTfcEAqjwHSPAQXX7vk8BOI777xz3GRs/4+86aabQuADxMsvv5x23XXXPpznnntuGIwA4aTI/Gf5vvvuGwqjwHSPAQXX7vk8BGKWD20i9vn5558fAh8gHnjggSLGQw89NAxGgOyxxx5FnNu2bQuFU2C6xYCCa7f8HQYt///0QdW2f/azn4XB+Morr/Qtl4Jz6dKlYTACZNGiRX2+XLBgQSiMAtM9BhRcu+fzMIjPOOOMcZPySSedFAabAbniiivGYZw/f3564okn7HCIfPPmzenNb37zOJw33nhjCGwC0V0GFFy76/sQyH/5y1+mb3zjG4mnhqMmXqzAMvh1112XXnrppZAwn3nmmfTDH/4wcTLxyCOPhMQoUN1iQMG1W/4WWjEgBsSAGNgBDCi47gCS1YQYEANiQAx0iwEF1275Oxza5557LvFw0z//+c9w2Dwg/gv68MMP+6Jw2zwdfc8994TDJUDdZEDBtZt+D4GatxbZU8LkF154YQhcHsQdd9yR9txzzzGcER/a4qPwRx111BjG/fffP917772eBm2LgeoYUHCtzmUyGAbuv//+scnYB9jf/OY3oQjae++9+3BefPHFoTCeddZZfRgJtkpioGYGFFxr9l6Hbb/yyiv7JmSCbKTAwyfY/ImDbS9cuDCU5+fMmVPE+cILL4TCKTDdYkDBtVv+DoP25ptvLk7IV111VRiM3E+2gOrzU089NQxGgHCy4PGxPXv27FAYBaZ7DCi4ds/nYRAfcsgh4yblffbZJ/3nP/8Jgw8gvI0pDzw8wBUpXX/99X0YL7300kgQhaWDDCi4dtDpUSA///zz6YILLkjHHnts+vKXv5z4bFnE9L3vfa/3cvvPfvaz6be//W1EiOm2225Lp59+evrkJz+Z1q1bFxKjQHWLAQXXbvlbaMWAGBADYmAHMKDgugNIVhNiQAyIATHQLQYUXLvl75Bo+XqMkhgQA2KgTQwouLbJG7JlQgz86le/SocffnjvYZiDDz443XLLLROqX4Mw95FPPvnk9PrXvz7ttdde6Vvf+lYNZk/Yxq985SvpbW97W9pll13S5z73ufS///1vwjpUQQy0iQEF1zZ5Q7aMzACvO2Qizp+kjfaKwGOOOaYP49VXXz0yTzUIfv3rX+/DyOcElcRAzQwouNbsvQ7bfs011/RNyATalStXhmFl69atRYzHHXdcGIwAec973lPEqavXUG7uHBgF1865PAbga6+9tjghf/vb344BMKXeR9HzK3P2jz/++DAYAcK7hEs4X3755VA4BaZbDCi4dsvfYdA+/fTTabfdduublKN9aJur1DzwcGIRKfGx+xzjmWeeGQmisHSQAQXXDjo9CmRe0n/kkUf2HvbhwaYNGzZEgTaG45lnnum9XIETifnz54da9h4DmVLvi0Z8/Wf33XdP5557rj+kbTFQJQMKrlW6TUaLATEgBsRAmxlQcG2zd2SbGBADYkAMVMmAgmuVbpPRYkAMiAEx0GYGFFzb7B3ZNpAB7kfy8oEjjjginXfeeb2nawdWqPTg6tWrEw82LV68OG3cuLFSFIPNXr9+fe9lGSeccEJau3btYGEdFQMVMKDgWoGTZGKZgYMOOmjcU6bvete70osvvlgWrrT07LPPHoeRp2p5M1WkdN111/VhXL58eSSIwtJBBhRcO+j0CJBvuummvgmZwPODH/wgArweBq7M87+osH/KKaeEwQgQe4Wlx/qWt7wlFEaB6R4DCq7d83kIxGvWrCkGHl6lFyU99NBDRYwLFy6MArGHY+7cuUWc27dvD4VTYLrFgIJrt/wdBu2DDz5YnJCjfUx8v/3268N56aWXhvEjQM4555w+jEcffXQojALTPQYUXLvn8zCIV61alV73uteNTcyRrlrNSbwoY968eWMYTz31VDsUJn/hhRd6D2zZsvAHPvCB9Je//CUMPgHpJgMKrt30exjUPMB09913p23btoXBVALypz/9KT3++OOlQ2HK/va3v6UHHnggDB4B6TYDCq7d9r/QiwExIAbEwAwwoOA6A6RKpRgQA2JADHSbAQXXoP7nc118PYUvjvzud78LijKlX/ziF+miiy5KN998c1iM99xzT1qxYkW66qqrwv2P15z25JNPpiuvvDLxycC//vWvVhwu/8lPfpIuueSSdOedd4bDJkDjGVBwHc9HiD0+x5Z/gDrin/JPO+20sQd9eBjmxBNPDOE/D4KHtuxBH3L+tvLoo496keq3//CHP/R9PvCGG26oHpcH8Morr/T9n/eLX/yiF9F2MAYUXIM5FDjnn3/+uAnZJmeCbpTEmb/h8jkvl4iSWH3Ydddd+3BG+yQbJ0Xeh2zvu+++UdzYw8ErLHOM7PNfZqWYDCi4BvRr6QPbDGT+1hElXX755cXJihOLKIknZ0sT8mGHHRYFYg/HHnvsUcQZ6Qnwz3zmM0WMN954YyhfCsyrDCi4vspFmK0LL7ywOJCfffbZMBjvuuuuIsZI915ZSuQj6XmAXbp0aRg/AmTRokV9GBcsWBAK43e/+90+jPiVvx8pxWRAwTWgX//1r3+l/KX2PNgULS1ZsmTchPWJT3wiGsR0xRVXjMM4f/78cF//4YEt3iXsTyIiXtHx9SaP8Utf+lK4/ipArzKg4PoqF+G2eChk5cqVafPmzeGwGaA77rgjffOb30wbNmywonD5fffdl3iwad26dem///1vOHwAYlWFp6F5Yvjvf/97SIyA4pmAyy67LEV7TWdYh00BmILrFMhTVTEgBsSAGBADJQYUXEusqEwMiAExIAbEwBQYUHCdAnltr/rII4/0lp/4S0fUxHLixo0bEy8hiJz4L2j0v23cf//9oW9h0D+3bt2aNm3alP79739H7q7CllJScA3aDRYvXjz28AQPi0T6/6e5jHtX/gGRCy64wA6FybmnvOeee47hPOmkk8JgMyCcIB111FFjGHkByp///Gc7HCbn/8nWX3fZZZe0du3aMNgEpJ8BBdd+Tqov+c53vjM2iG0wz549O/HXjiiJh3wMm88j/ZcXX+299959OC+++OIobuzhOOuss/owEmwjpeuvv74P42te85oU6cUukfw1HVgUXKeDxZbpKL3xhgD0+9//vmWWTt4cnir1QdW2IwWeLVu2FDEuXLhw8sS1sOacOXOKOPnOa5RUOoGgz956661RIApHxoCCa0ZIhF2//GRBhzzSO2l5WYTHZtv8nSNKeu6554oYo30w/cMf/nAfzre+9a1R3NjDwbu9rY/6PPLf5EI5cBJgFFwnQVrbq/Bh7de+9rXjBjP3YKOlQw89dBxG3kf70ksvhYL5hS98YRxGJuZoS9/8H9sHHLajvfSEB5nyF2WccMIJofqqwIxnQMF1PB9h9giw55xzTmIA89LwiGn79u3pa1/7WuJdyl/96lfTU089FRFm+v73v997RSBLi5GW9r2zbr/99sT7dz/1qU+lH//4x/5QmO2HH344LVu2LH3sYx/rfUIwDDABKTKg4FqkRYViQAyIATEgBibPQDG48nHtSPfnSvSAMfJHxMHMa+SiYwQnGKO+FtD6Lhh5QjpyAmP0/srqSnSMNiYjfSikNO6G9ddicF2xYkX44Przn/883XbbbSXOwpQRXPkvaPT0+c9/PnxwXbNmTfjgypeOfvrTn4burgRXvloVPXGbJnpw5V3fg06UFFwD93IF1zjOVXCN4UsF1xh+BIWCa4MvdeXaQEyFxbpyrdBpBZN15VogpdIiXbk2vP5Qy8KV9ujMbF25ZoRUvKsr14qd50zXlasjo/LNSV25Ll26NB1++OHpox/9aNjf+973vnTAAQeExYfv8OG8efNCYwTnO97xjt67aSP313322Sfxv97IGN///ven/fffPzRGXpjxzne+MzRG+ihv3frIRz4SGueCBQsmfs+VZbZDDjkk0RGi/iCGF4RHxQeugw8+uDeQI2ME29vf/vbEKwEj4+QkieATGeN73/vexItAImM87LDD0l577RUaI/7jYxMf/OAHQ+PkhFcPNBWWH3TPtUBKpUW651qp4zKzdc81I6TiXd1z1T3XirvvcNN1z3U4R7VI6J5rLZ4abKfuuQ7mp6ajk7rnqgeaanJxs60Krs3c1HZEwbU2j5XtVXAt81JjqYJrg9e0LNxATIXFWhau0GkFk7UsXCCl0iItCzcsC/PVjeivPwRjtK+L5OOQK9foGMEMxuivPwRj9NcfgjF6f+XKNTpGG5PR39CEHyf8QFM+SWtfDIgBMSAGxIAYGJ2B4usPR68uSTEgBsSAGBADYiBnQME1Z0T7YkAMiAExIAamyICC6xQJVHUxIAbEgBgQAzkDCq45I9oXA2JADIgBMTBFBhRcp0igqosBMSAGxIAYyBnoC66PP/54OvDAA9NFF12Uy2q/EgZ4RPzII49Ms2bN6v3w57333luJ9TLTGGAsLlmyZMyP+JN9pboZ2LZtW9p99901x1bqxo9//OPjxiTjshQvxwXX9evX975mcMQRRxSFK+Wic2YvW7Zs3H/p2J87d27neKgdMCdEDFomYxI5X3JatWpV7dA6bT+TM1+NKU3InSamEvDEx1H+qzwuuJ5xxhm9KxycLsdX4ukRzGRS5uxKqX4GGJdMzkp1MnDttdcmu3jRHFunDycVXA2qgqsxESPnCuhNb3pTDDAdRsFJEisQTNBK9THAMj9XrOSaY+vzn1nMXDrhK1erLMcbEzFyrnR0llyvL/Ed91pZEpYf6/UjVzzceiNpjq3XjwRX7pmzGkjO2LRbNx5Vca1QjvcU1b2NL5mUleplwMYjt2248tHDafX5Eh/65XzzaX1IZLEPpKxCcNLEA6R5UnDNGQm0z/IhgdV3hkDwOgmFh5n0cFpdrudkiCucW2+9NW3atKn342qHH/tKdTOAf0vPtCi41u3XRusVWBupqfoA93pKA7lqUMGNt4eYuMKxHysQ/NhXqpsBBde6/Tch6xVYJ0RXa4VZcsoTS8N+eTE/rv06GNCycB1+yq1kFTBfCWRMlk6SdOWasxdgnyub0o8BrVQPAywBs5zI/Rx+LAcziPPBXQ8iWWoMKLgaE3XlXKXyQNMoY7IYXDljLp0110VDd61l6bD0k0/r6xP4zHwp/9XnvyaL8aX82cROu8s5uR1lTBaDa7uhyToxIAbEgBgQA+1mQMG13f6RdWJADIgBMVAhAwquFTpNJosBMSAGxEC7GVBwbbd/ZJ0YEANiQAxUyICCa4VOk8liQAyIATHQbgYUXNvtH1knBsSAGBADFTKg4Fqh02SyGBADYkAMtJsBBdd2+0fWiQExIAbEQIUMKLhW6DSZLAbEgBgQA+1mQMG13f6RdWJADIgBMVAhAwquFTpNJosBMSAGxEC7GQgRXP/xj3+kM888Mz322GOtZJuv1PDbEYmXvS9atKj3rUheMt2mxLtUly9fPimTeJ9nTe9ibRv3kyJ9mivtKP/RV6J93KC2/j/NXadKdSGC65YtW3pfgdm8eXMrnWDfcJxp4/j0EV9ssC9utG2C52XXk/0WKZj4QkwNiRMccLaN/53NHZzAzUwnPslX+gTYTLc7k/pr6v8zyUNNuhVcp9FbnF2WBvWOCq5MXqNcIfOR5plOBxxwQO/LEb6dqQRX6jLBtC2VcBJUly1bNmOmcgJVY4KTHXHCwRjYEUF8pnxQ8u/O6v9w2cZxN1PcT6deBddpZJOOuLOCK0tuBFcG4aBkcoNkpnqMk4ySLVMJrlO1aSbqN+GcibZM5/r16yd99W86lLeXgbb5l9UwBdfJ9ZfQwZWOykdtmejJV69ePY4lzqKXLFnSu5fHfUrk+CC1lXlhghIyHDd99sFcO1Nm2dJ/3Jpykl25Ys+BBx7Yq0/O/Ucm6GGJoERb6Db7fD3a8XqRtba9bvTk9vsrLHSCHRl+4C3dJzNeDavn1beBTdhibVhwNS49nlI73nbwmB7K8R26zWZ08cPmUa6OfD3D6jktTSrYSJvgH4TTbPP20wcoP++883p2Wh9CT56Qs/5ocpRxNQZGK2vys+ljUrR+YRh9e7lNg/jzNqETHJ4v3yZtYSP64NES7eX9Er3gQNb0mrzlJRzUa0r0E99XrO94DNhYGuclnb4euLDT8wgPNjeY3pwb4xosxo/1JWtzkH8Ng8kabzaWjG/zSz7X+DFqOrAxH+/ebnyHXuzFVn6ed5sHkOFY3gay+MHaQQ4eSFZmXMAptvj2zc5a87DBFcezvEKHZSDQOe1+pDmLchzOMimdnn3qsdSHsy3hcDoBnY3OzL51PORJdCTKbJkQXRYw6FBMHrSDPMewK7fH2vM58tiIbm8f+qwj0jb6kDO81rbXRZnJoYufHyzYjq12zOy2dtBl9lg7Oa++DZOxNtCLjbQziG9vs20jbwOTMtOFn0wXZejGV95m0+HzYVhNP7kl2jcbRsFp9cjBja3cD0QnP7Yp975iG9/SjvUVm6Csj1HHdPi6vj24p3/hH5NFj5c3m0p9y8uZTbkcE6pP6KdNctqkbX6WaA9fWUKGMpMHL2OEdiwhj07jgpzj3j6Ttdz7iTJ00A66rU9aWzkG02G5YUencYk+a59+Zv4ynpGlD/pE+5R5/4ODcuqRBvmXNtFrybijzDBhH1yByc81ht/aQQd2Yw/1c7tt7FDOODG/s2/H4I+2rG3rb7RlCXnjBtzmQ47TLrqtbWz3fjcdNedhgyudyzsaJ7GPsy3hWDq3nwA4Rieg3AaQyVnHsvrIIGsJ/X4AWDllXp+VM6n4IG7lPs8nGztGOfUtmY3kg5LJ5TLYjk6PkW0bQCZf4pWBVeI1t8Xazv2S821t+TzntkkXPoPrvO1c1yhY4Rdc8GCTh/UJ9JkNeVtW7tvEprxvoJdydFtiEmLSaUrwQJ1hibbQNSiVbEIen/uJju3cdgIB9e3EyXjPx5JvH3nve3T6dpC1vmB6kfH93Otr2qaOt9c4y22ztpr0UI599JWmhO78eMmvYM/l0EmZ58Rszduj3GOyPubrUgeuaCvvk/QpL8s2bWOrJbbz8U6bvh6yyDEufL+lHLnSPJD7GFls9HOn2RApHz5KK0CbPy1sHe9HP/pR2rRp09iPZQvf8UzOT5jAtXLroLbvOyJyeQehc/kBYNRRVpowkUdHU7IJy+zwcgwiH5jNxpKsr2dyvoxtbOSM1/PFtl1tIWN14dHLNfGa22L1beI0GwbhNJmcW9OVt4G897HV9/koWE0ev8ELk0Y+GTTZYOWmgxybwJCnfNJrkrN6w/qMyRFI0DXo1kNTW/Qt34+RY8nO+5xtX5+Jlv1Bycsjxz72lfQa14Z3EI68TWz39puOfPyan0p9yHQSbEp+s+O0w5JwjoGrQn9SkGP39f1JkNlqxy2n3GNqsr2pfs4J+03j3QdD5HL81nbT/Grj2+Rs37CQo5cxhY6oafBoqAR1U3ClQ5d+NpjM+TlMKzc5O6NjgrFEh2Pg+QGbDwCTzTu2lTcNBDtudpQ6Z17XZM1m05HnJpeXcxZb4ooy7CdZ3SY5a9vkbN/asnLb9zk6c3l/POfWdJXqDNM1ClZr29oxDqyc3I7lNli5l8UmCxi+HL1gszTM9tzvVq+U055hpe/m/ajJprwN5Jp+Zjs5bQ1K6DB542iYXvRxouBx5CfDeZv5eMvxmLzZkPvPjpNjX37Fmx9vwuD7jMfu649qKxi8vibbm7Dm7TB3jWI39cxnZreduDXVNz7NRqvnc+ZN9GIHQXYiJ09eT5u3QwfXYYOwyflWbp0EBzIx+c7E2WY+WeUDwByfd2wrbxoIdrxkhx2zjmn7g2RNhtzkfBnb2OjPtPPjvu6ovHr+fP2SbrjN5b1czq3hKNUZpmsUrNY2fraJPfd3kw1WbjrIm2zKJy/kBk3mw/qMb9O2sYd2chvYR1+eKPMrLcNsoj51/JJgrpN9394oqxW5Dk4WwEE7Jb+bPDL8LDVxZn4apMvbbPp8Tt8ocehl2G7SM6qttOExNdnehDVvJ18xye21ferl+Kxtf2Fh8j43OV+Wb6PDTp642h+mM6/f5v2QwdUG7qBJCqc0Od/KyS0RePzyjZX7nE7ol2rtWN6xrbxpINhxOlrTxIYtoww202W5YbN9y9FXst2Ok0+UV88f9Zva5hg4c3nfNlyNineYrlGw0radoRNU8T/8+MFveHK7rdzb32RTPnlxJu+X5bwOtof1mVze79OW78PYVDqhQs5zTQAZZBNtGFeDTrxoD/stgbXUvh1vygkMg+zJ7W/izPyU+8+3O6wt+GR5dVjKsZv8qLaO2v+bsObtjDoGqOd9ht12oVFaiTFc5MavL2vaHjTXNdVpe3nI4ArpDD7OhPKrDb/f5Hwr94OOTubvO5UmEbvv5CdgbMk7tnWKpoFgxz0O3x6dOp+sSzZ7PbZtcvnAsAHDo/w+0a5vexRekce+/OTG2vb6bTvHY+WWjzq5ID9Ml2FlKcon7Dbfsc0Vkj20QTlBxgeDieBssimfvMBJu76fYqPZZRzS9qCU10eWQOHtx6a8LQuSvn+UytDn+TJ+uP9otiLjt2nPT9SGFUw+edv9tuljXHs9vi7b+XhDlrbzZFzm7Xs5w57LGC7Tkf8NxXODvhy7tZHbavpy/4IBWUsml9vVhLWpnWF2U6900k1wLs2v3h6z0Wz2ee5X9uHI1/fyNW7397gKUeT3XIFA56dj4DA6hz2UwtmypSbnW7l3tAVO9PmfD0a0iX46He1ZcMk7trXfNBDsOLnHgU6w0L6fJJEr2ez1+G3sYVJFn9djE4kds7YswOT2eF6xySfj3rdhNno526a+59vKLR91ckF+mC5kmrCaDSWfmf0+8IyKs8km6oPNJyYu5I1fX5f+QJA0H3n/eR3oNRl8QJ/k5ID6ltDLyRJ9dlDfQp52kLe+Tc6+nyTZpg1rF/uxwxLyOVba93qpy76lHAfHwe9xmKzl1PHtNo0z86f53OrneclGX8fmBsNt3HiZEnbayW2lrOTfUft/E9ZSO/kYKNltHFlfNH9bPwSXHQP/KPMrGL3P6Xvsw3Ok9GovrhjV9u3b0+23314ccHQOOhw/tv2gZNsPAKPAyk2WiYUO72U5ZoPKOhz1KafT0p6dfXLcy1g7HPc6rbyUU5/2+JleL5fb7I+VtgkQxok/jm6zn7xkN/LY3cSr6TMZw2g22nGfI8PxpoRd3hbTVaozTJe10YR1kG5s8HagaxScTTahq+RPyuEXf+ftYZ/5Lz9m2Mwu6zO0nycmNMqNh0H+pi5toQ+7aL9kt3FXkrG2cjtyvblPqTcIR0mf5wU7S/jN1ry9XJ9hN3+UdBmHyMBjzs0g7N5W2sKe3L/o83JNtjdhpa6vbxhzu5tkjP+cK3CBmR/b/rjZaG353I4ZX6V2vXyN2yGC60wTzyREZy8lm6BKx1QmBtrMgPpum70j22pnQMF1BA+y1MEZVp4o45g/W8tltC8G2sqAgmtbPSO7IjCg4DqCF7lqJYja/SbuEXB/gftLEZczRqBEIgEYUHAN4ERBaC0DCq4TcA33FOynoDoB4iTaSgbye2StNFJGiYFKGVBwrdRxMlsMiAExIAbay8D/AQh/63HGPg2ZAAAAAElFTkSuQmCC[/img][/td][td]mean: 3.02 cm[br][br]standard deviation: 0.55 cm[/td][/tr][/table][br][br][table][tr][td][img]data:image/png;base64,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[/img][/td][td]mean: 2.32 cm[br][br]standard deviation: 0.13 cm[br][/td][/tr][/table][br][br]Compare the two dot plots using the shape of the distribution, measures of center, and measures of variability. Use the situation described in the problem in your explanation.
[size=150]He buys [math]f[/math] bags of fertilizer and [math]p[/math] packages of soil. He pays $5 for each bag of fertilizer and $2 for each package of soil, and spends a total of $90. The equation [math]5f+2p=90[/math] describes this relationship.[/size][br][br]If Kiran solves the equation for [math]p[/math], which equation would result?
[size=150]Elena wanted to find the slope and y-intercept of the graph [math]25x-20y=100[/math]. She decided to put the equation in slope-intercept form first. Here is her work:[br][center][math]\displaystyle \begin{align} 25x-20y &= 100 \\ 20y &=100-25x \\ y &= 5-\frac54x \\ \end{align}[/math][/center]She concluded that the slope is [math]-\frac{5}{4}[/math] and the [math]y[/math]-intercept is [math]\left(0,5\right)[/math].[br][/size][br]What was Elena’s mistake?
What are the slope and [math]y[/math]-intercept of the line? Explain or show your reasoning.[br]
[size=150]Andre is buying snacks for the track and field team. He buys [math]a[/math] pounds of apricots for $6 per pound and [math]b[/math] pounds of dried bananas for $4 per pound. He buys a total of 5 pounds of apricots and dried bananas and spends a total of $24.50.[/size][br][br]Which system of equations represents the constraints in this situation?
[size=150]Equation 1: [math]y=3x+8[/math][br]Equation 2: [math]2x-y=-6[/math][/size][br][br]Without using graphing technology:[br]Find a point that is a solution to Equation 1 but not a solution to Equation 2.
Without using graphing technology:[br]Find a point that is a solution to Equation 2 but not a solution to Equation 1.[br]
Find a point that is a solution to both equations.[br]