two linear equations are shown. what is the solution to the system of equations? y = 1/3x + 2 y = 4/3x - 5

Explanation:

Step1: Set the two equations equal

Since the solution of the system is where the two lines intersect, we set $\frac{1}{3}x + 2=\frac{4}{3}x - 5$.

Step2: Solve for x

First, subtract $\frac{1}{3}x$ from both sides: $2=\frac{4}{3}x-\frac{1}{3}x - 5$. Then simplify the right - hand side: $2 = x-5$. Add 5 to both sides to get $x = 7$.

Step3: Solve for y

Substitute $x = 7$ into the first equation $y=\frac{1}{3}x + 2$. So $y=\frac{1}{3}\times7 + 2=\frac{7}{3}+2=\frac{7 + 6}{3}=\frac{13}{3}$.

Answer:

$(7,\frac{13}{3})$