Question

spiral review
problems 8–9: solve each system of equations. show your thinking.
8.
\

$$\begin{cases} y = 7x + 10 \\\\ y = -4x - 23 \\end{cases}$$

9.
\

$$\begin{cases} y = 3x - 6 \\\\ y = -2x - 1 \\end{cases}$$

Explanation:

Step1: Set equations equal (Problem 8)

Since $y = 7x + 10$ and $y = -4x -23$, set them equal:
$7x + 10 = -4x -23$

Step2: Solve for x (Problem 8)

Combine like terms:
$7x + 4x = -23 -10$
$11x = -33$
$x = \frac{-33}{11} = -3$

Step3: Find y (Problem 8)

Substitute $x=-3$ into $y=7x+10$:
$y = 7(-3) + 10 = -21 + 10 = -11$

Step4: Set equations equal (Problem 9)

Since $y = 3x -6$ and $y = -2x -1$, set them equal:
$3x -6 = -2x -1$

Step5: Solve for x (Problem 9)

Combine like terms:
$3x + 2x = -1 + 6$
$5x = 5$
$x = \frac{5}{5} = 1$

Step6: Find y (Problem 9)

Substitute $x=1$ into $y=3x-6$:
$y = 3(1) -6 = 3 -6 = -3$

Answer:

Problem 8: $x=-3$, $y=-11$
Problem 9: $x=1$, $y=-3$