Question

solve the system of equations graphed on the coordinate axes below.
y = -2x - 7
y = \frac{1}{2}x + 8

Explanation:

Step1: Set the two equations equal

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

Step2: Move $x$ - terms to one side

Add $2x$ to both sides: $-7=\frac{1}{2}x+2x + 8$. Combine like - terms: $-7=\frac{1 + 4}{2}x+8$, so $-7=\frac{5}{2}x + 8$.

Step3: Move the constant to the other side

Subtract 8 from both sides: $-7 - 8=\frac{5}{2}x$, so $-15=\frac{5}{2}x$.

Step4: Solve for $x$

Multiply both sides by $\frac{2}{5}$: $x=-15\times\frac{2}{5}=-6$.

Step5: Find $y$

Substitute $x = - 6$ into $y=-2x - 7$. Then $y=-2\times(-6)-7=12 - 7 = 5$.

Answer:

$x=-6,y = 5$