solve the following system of equations graphically on the set of axes below.\n$y=-x - 2$\n$2x - y=8$\nplot…

Explanation:

Step1: Rewrite the second equation in slope - intercept form

Starting with $2x - y=8$, we can solve for $y$. Subtract $2x$ from both sides: $-y=-2x + 8$. Multiply both sides by $- 1$: $y = 2x-8$.

Step2: Identify key points for the first line

For the line $y=-x - 2$, when $x = 0$, $y=-2$ (y - intercept). When $y = 0$, $0=-x - 2$, so $x=-2$ (x - intercept).

Step3: Identify key points for the second line

For the line $y = 2x-8$, when $x = 0$, $y=-8$ (y - intercept). When $y = 0$, $0=2x-8$, then $2x=8$ and $x = 4$ (x - intercept).

Step4: Find the intersection point

Set the two equations equal to each other: $-x - 2=2x-8$. Add $x$ to both sides: $-2=3x-8$. Add 8 to both sides: $6 = 3x$. Divide both sides by 3: $x = 2$. Substitute $x = 2$ into $y=-x - 2$, we get $y=-2 - 2=-4$.

Answer:

The solution of the system of equations is $(2,-4)$.