Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{1}{2}x + 7$
$y=-2x - 8$
plot two lines by clicking the graph. click a line to delete it.

Explanation:

Step1: Set the two equations equal

Since $y$ is equal in both equations, we set $\frac{1}{2}x + 7=-2x - 8$.

Step2: Solve for $x$

Add $2x$ to both sides: $\frac{1}{2}x+2x + 7=-8$. Combine like - terms: $\frac{1}{2}x+\frac{4}{2}x+7=-8$, so $\frac{5}{2}x+7=-8$. Subtract 7 from both sides: $\frac{5}{2}x=-8 - 7=-15$. Multiply both sides by $\frac{2}{5}$: $x=-15\times\frac{2}{5}=-6$.

Step3: Solve for $y$

Substitute $x = - 6$ into $y=-2x - 8$. Then $y=-2\times(-6)-8=12 - 8 = 4$.

Answer:

The solution of the system is $x=-6,y = 4$