Question

solve the following system of equations graphically on the set of axes below.\\(y = -x + 2\\)\\(x - 2y = -10\\)plot two lines by clicking the graph.\click a line to delete it.

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

Rearrange $x-2y=-10$ to $y=mx+b$ form:

$$\begin{align*} -2y&=-x-10\\ y&=\frac{1}{2}x+5 \end{align*}$$

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

Identify intercepts:

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

Step3: Find points for $y=\frac{1}{2}x+5$

Identify intercepts:

• When $x=0$, $y=5$ (point $(0,5)$)
• When $y=0$, $0=\frac{1}{2}x+5 \implies x=-10$ (point $(-10,0)$)

Step4: Find intersection algebraically

Set equations equal:

$$\begin{align*} -x+2&=\frac{1}{2}x+5\\ -\frac{3}{2}x&=3\\ x&=-2 \end{align*}$$

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

$$ y=-(-2)+2=4 $$

Answer:

The solution (intersection point of the two lines) is $(-2, 4)$.
To plot the lines:

1. For $y=-x+2$, plot points $(0,2)$ and $(2,0)$, then draw the line through them.
2. For $y=\frac{1}{2}x+5$, plot points $(0,5)$ and $(-10,0)$, then draw the line through them. The lines cross at $(-2,4)$.