Question

1. $-x + y = 2$

$3x - 5y = -4$

Explanation:

Step1: Isolate y in first equation

From $-x + y = 2$, rearrange to get $y = x + 2$.

Step2: Substitute y into second equation

Substitute $y = x + 2$ into $3x - 5y = -4$:
$3x - 5(x + 2) = -4$

Step3: Simplify and solve for x

Expand and combine like terms:
$3x - 5x - 10 = -4$
$-2x - 10 = -4$
$-2x = -4 + 10$
$-2x = 6$
$x = \frac{6}{-2} = -3$

Step4: Solve for y using x value

Substitute $x = -3$ into $y = x + 2$:
$y = -3 + 2 = -1$

Step5: Verify solution

Check in $3x - 5y = -4$:
$3(-3) - 5(-1) = -9 + 5 = -4$, which matches.

Answer:

$x = -3$, $y = -1$