Question

1. $-x + y = -2$; $2x - y = 6$

Explanation:

Step1: Add the two equations

We have the system of equations:
$$-x + y = -2$$
$$2x - y = 6$$
Adding them together: $(-x + y)+(2x - y)=-2 + 6$
Simplify left side: $-x + y+2x - y=x$, right side: $4$. So $x = 4$.

Step2: Substitute x into first equation

Substitute $x = 4$ into $-x + y=-2$:
$-4 + y=-2$
Add 4 to both sides: $y=-2 + 4=2$

Answer:

The solution to the system of equations is \( x = 4 \), \( y = 2 \) (the point \((4, 2)\) is the solution as it satisfies both equations).