Question

solve the system of equations graphed on the coordinate axes below. y = x - 2 y = -\frac{1}{5}x - 2

Explanation:

Step1: Set the two equations equal

Since $y = x - 2$ and $y=-\frac{1}{5}x - 2$, we set $x - 2=-\frac{1}{5}x - 2$.

Step2: Add $\frac{1}{5}x$ to both sides

$x+\frac{1}{5}x - 2=-\frac{1}{5}x+\frac{1}{5}x - 2$, which simplifies to $\frac{5x + x}{5}-2=- 2$, or $\frac{6x}{5}-2=-2$.

Step3: Add 2 to both sides

$\frac{6x}{5}-2 + 2=-2 + 2$, getting $\frac{6x}{5}=0$.

Step4: Solve for x

Multiply both sides by $\frac{5}{6}$, so $x = 0$.

Step5: Find y - value

Substitute $x = 0$ into $y=x - 2$, then $y=0 - 2=-2$.

Answer:

$x = 0,y=-2$