IM Alg1.2.14 Practice: Solving Systems by Elimination (Part 1)

Which equation is the result of adding these two equations?

[math]\begin{cases} \text-2x+4y=17 \\ 3x-10y = \text-3 \end{cases}[/math]

[math]-x-6y=14[/math] [math]x-6y=14[/math] [math]5x+14=20[/math] [math]-5x-6y=14[/math]

Which equation is the result of subtracting the second equation from the first?

[math]\begin{cases} 4x-6y=13 \\ \text-5x+2y= 5 \end{cases}[/math]

[math]9x-8y=8[/math] [math]-x+4y=8[/math] [math]-9x-4y=8[/math] [math]x-4y=8[/math]

Solve this system of equations without graphing:

[math]\begin{cases} 5x+2y=29 \\ 5x - 2y= 41 \\ \end{cases}[/math]

Here is a system of linear equations:

[math]\begin{cases} 6x+21y=103 \\ \text-6x+23y=51 \\ \end{cases}[/math][br][br]Would you rather use subtraction or addition to solve the system? Explain your reasoning.

[size=150]Kiran sells [math]f[/math] full boxes and [math]h[/math] half-boxes of fruit to raise money for a band trip. He earns $5 for each full box and $2 for each half-box of fruit he sells and earns a total of $100 toward the cost of his band trip. The equation [math]5f+2h=100[/math] describes this relationship.[br][/size][br]Solve the equation for [math]f[/math].

Match each equation with the corresponding equation solved for a.

[size=150]The volume of a cylinder is represented by the formula [math]V=\pi r^2h[/math].[/size]

Find each missing height and show your reasoning.

Match each equation with the slope m and y-intercept of its graph.

Solve each system of equations.

[math]\begin{cases} 2x+3y=4 \\ 2x = 7y + 24\\ \end{cases}[/math]

[math]\begin{cases} 5x + 3y= 23 \\ 3y = 15x - 21 \\ \end{cases}[/math]

Elena and Kiran are playing a board game. After one round, Elena says, "You earned so many more points than I did. If you earned 5 more points, your score would be twice mine!"

[size=150]Kiran says, "Oh, I don't think I did that much better. I only scored 9 points higher than you did."[/size][br][br]Write a system of equations to represent each student's comment. Be sure to specify what your variables represent.[br]

If both students were correct, how many points did each student score? [br]