Question

solve the system of equations graphed on the coordinate axes below.
y = -\frac{2}{3}x + 4
y = \frac{1}{2}x + 4

Explanation:

Step1: Set the two equations equal.

Since both equations equal $y$, we set $-\frac{2}{3}x + 4=\frac{1}{2}x + 4$.

Step2: Move the $x$ - terms to one side.

Subtract $\frac{1}{2}x$ from both sides and subtract 4 from both sides: $-\frac{2}{3}x-\frac{1}{2}x=4 - 4$.

Step3: Find a common denominator for $x$ - terms.

The common denominator of 3 and 2 is 6. So $-\frac{2}{3}x-\frac{1}{2}x=-\frac{4}{6}x-\frac{3}{6}x=-\frac{7}{6}x$, and $4 - 4 = 0$. We have $-\frac{7}{6}x=0$.

Step4: Solve for $x$.

Multiply both sides by $-\frac{6}{7}$ to get $x = 0$.

Step5: Find the value of $y$.

Substitute $x = 0$ into either of the original equations. Using $y=\frac{1}{2}x + 4$, we get $y=\frac{1}{2}(0)+4=4$.

Answer:

$(0,4)$