Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{1}{2}x + 6$
$y = -\frac{5}{4}x - 8$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection by solving equations

Set $\frac{1}{2}x + 6 = -\frac{5}{4}x - 8$.
Multiply all terms by 4 to eliminate denominators: $2x + 24 = -5x - 32$.

Step2: Solve for x

Add $5x$ to both sides: $2x + 5x + 24 = -32$ → $7x + 24 = -32$.
Subtract 24 from both sides: $7x = -32 - 24$ → $7x = -56$.
Divide by 7: $x = -8$.

Step3: Find y using x = -8

Substitute $x = -8$ into $y = \frac{1}{2}x + 6$: $y = \frac{1}{2}(-8) + 6 = -4 + 6 = 2$.

Answer:

The solution is $x = -8$, $y = 2$ (the intersection point is $(-8, 2)$).