Question

solve the system of equations by graphing. graph systems on your recording sheet. enter answer here. enter your answer as a ordered pair (x,y), no solution, or infinitely many solutions. \

$$\begin{cases} x + y = 2 \\\\ x - y = 4 \\end{cases}$$

Explanation:

Step1: Rewrite equations in slope-intercept form

For $x+y=2$:
$y = -x + 2$
For $x-y=4$:
$y = x - 4$

Step2: Find intersection via substitution

Set $-x + 2 = x - 4$
$2 + 4 = x + x$
$6 = 2x$
$\frac{6}{2}=x$
$x=3$

Step3: Solve for y using x=3

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

Answer:

$(3, -1)$