Question

$x + y = 2$
$y = -2x + 3$
click to select points on the graph.

Explanation:

Step1: Rewrite first equation to slope-intercept

Rearrange $x + y = 2$ to solve for $y$:
$y = -x + 2$

Step2: Find points for $y=-x+2$

Choose $x=0$: $y = -0 + 2 = 2$, point $(0, 2)$
Choose $x=2$: $y = -2 + 2 = 0$, point $(2, 0)$

Step3: Find points for $y=-2x+3$

Choose $x=0$: $y = -2(0) + 3 = 3$, point $(0, 3)$
Choose $x=1$: $y = -2(1) + 3 = 1$, point $(1, 1)$

Step4: Find intersection of the two lines

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

Answer:

The solution to the system is the point $(1, 1)$. To graph:

1. Plot points $(0,2)$ and $(2,0)$, draw the line for $x+y=2$.
2. Plot points $(0,3)$ and $(1,1)$, draw the line for $y=-2x+3$.
3. The lines intersect at $(1, 1)$.