Question

Solve the system by substitution. Check your answer.
3x + 4y = 2
x = 5y +7

Answer 1

x = 2, y = - 1

Explanation:

Given the 2 equations

3x + 4y = 2 → (1)

x = 5y + 7 → (2)

Substitute x = 5y + 7 into (1)

3(5y + 7) + 4y = 2 ← distribute and simplify left side

15y + 21 + 4y = 2

19y + 21 = 2 ( subtract 21 from both sides )

19y = - 19 ( divide both sides by 19 )

y = - 1

Substitute y = - 1 into (2) for corresponding value of x

x = 5(- 1) + 7 = - 5 + 7 = 2

As a check

Substitute x = 2, y = - 1 into the left side of (1)

3(2) + 4(- 1) = 6 - 4 = 2 = right side

Solution is x = 2, y = - 1