[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]

[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 both equations.