Question

1. \

$$\begin{cases} 2x - 7 = -y \\\\ -5x + 13 = y \\end{cases}$$

(2, 3)

Explanation:

Step1: Substitute y into first equation

Substitute $y = -5x + 13$ into $2x - 7 = -y$:
$2x - 7 = -(-5x + 13)$

Step2: Simplify the equation

Expand and rearrange terms:
$2x - 7 = 5x - 13$
$13 - 7 = 5x - 2x$
$6 = 3x$

Step3: Solve for x

Isolate x by dividing:
$x = \frac{6}{3} = 2$

Step4: Solve for y

Substitute $x=2$ into $y=-5x+13$:
$y = -5(2) + 13 = -10 + 13 = 3$

Step5: Verify the solution

Check if $(2,3)$ satisfies both equations:
For $2x - 7 = -y$: $2(2)-7 = -3$, $-3=-3$ (true)
For $-5x +13 = y$: $-5(2)+13=3$, $3=3$ (true)

Answer:

The ordered pair $(2, 3)$ is a valid solution to the system of equations.