Question

what is a solution for the system of equations $x - y = 2$ and $y = 2x - 4$? \\(\bigcirc\\) $(4, 2)$ \\(\bigcirc\\) $(2, 0)$ \\(\bigcirc\\) $(3, 2)$ \\(\bigcirc\\) $(0, 2)$

Explanation:

Step1: Substitute y into first equation

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

Step2: Simplify and solve for x

$x-2x+4=2$
$-x=2-4$
$-x=-2$
$x=4$

Step3: Solve for y using x=4

Substitute $x=4$ into $y=2x-4$:
$y=2(4)-4=8-4=4$

Step4: Verify the solution

Check $(4,2)$ in $x-y=2$: $4-2=2$, which is true.
Check $(4,2)$ in $y=2x-4$: $2=2(4)-4=4$, which is true.

Answer:

(4, 2)