Question

What is the solution to the system of equations below? y = negative one-third x + 9 and y = two-thirds x minus 12 (21, 2) (21, –10) (–21, 16) (–21, –26)

Answer 1

Answer:

(21, 2 )

Step-by-step explanation:

Given the 2 equations

y = - $\frac{1}{3}$ x + 9 → (1)

y = $\frac{2}{3}$ x - 12 → (2)

Substitute (2) into (1)

$\frac{2}{3}$ x - 12 = - $\frac{1}{3}$ x + 9 ( add $\frac{1}{3}$ x to both sides )

x - 12 = 9 ( add 12 to both sides )

x = 21

Substitute x = 21 into either of the 2 equations and evaluate for y

Substituting into (2)

y = $\frac{2}{3}$ × 21 - 12 = 14 - 12 = 2

Solution is (21, 2 )