Question

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

Explanation:

Step1: Rewrite first equation

Rearrange $x+y=2$ to slope-intercept form:
$y = -x + 2$

Step2: Identify intersection via substitution

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

Step3: Solve for $x$

Isolate $x$ terms:
$-2x + x = 2 - 3$
$-x = -1$
$x = 1$

Step4: Solve for $y$

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

Step5: Find points for graphing (Line 1)

For $y=-x+2$:

• When $x=0$, $y=2$ (point $(0,2)$)
• When $y=0$, $x=2$ (point $(2,0)$)

Step6: Find points for graphing (Line 2)

For $y=-2x+3$:

• When $x=0$, $y=3$ (point $(0,3)$)
• When $y=0$, $x=\frac{3}{2}=1.5$ (point $(1.5,0)$)

Answer:

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

1. Plot points $(0,2)$ and $(2,0)$, draw a line through them for $x+y=2$.
2. Plot points $(0,3)$ and $(1.5,0)$, draw a line through them for $y=-2x+3$.
3. The lines intersect at $(1, 1)$.