Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{1}{2}x + 7$
$5x + 2y = -10$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

Solve $5x + 2y = -10$ for $y$:
$2y = -5x -10$
$y = -\frac{5}{2}x -5$

Step2: Find points for first line

For $y = \frac{1}{2}x +7$:

• When $x=0$, $y=7$ → $(0,7)$
• When $x=-4$, $y=\frac{1}{2}(-4)+7=5$ → $(-4,5)$

Step3: Find points for second line

For $y = -\frac{5}{2}x -5$:

• When $x=0$, $y=-5$ → $(0,-5)$
• When $x=-2$, $y=-\frac{5}{2}(-2)-5=0$ → $(-2,0)$

Step4: Find intersection algebraically

Set $\frac{1}{2}x +7 = -\frac{5}{2}x -5$
Multiply by 2: $x +14 = -5x -10$
$6x = -24$
$x = -4$
Substitute $x=-4$: $y=\frac{1}{2}(-4)+7=5$

Answer:

The intersection point (solution) is $(-4, 5)$.
To plot:

1. For $y=\frac{1}{2}x+7$: plot $(0,7)$ and $(-4,5)$, draw the line through them.
2. For $5x+2y=-10$: plot $(0,-5)$ and $(-2,0)$, draw the line through them.

The lines intersect at $(-4, 5)$.