Question

A system of equations is shown below:

6x = -7y + 11
5x + 2y = 13

What is the solution to this system of equations? (4 points)

(-3, 1)
(-1, 3)
(1, -3)
(3, -1)

Answer 1

6x + 7y = 11 . . . . (1)
5x + 2y = 13 . . . . (2)

6x + 7y = 11 (multiply through by 2) → 12x + 14y = 22 (
`1^(a)`)

5x + 2y = 13 (multiply through by 7) → 35x + 14y = 91 (
`2^(a)`)

by subtracting (
`1^(a)`) from (
`2^(a)`)

⇒ (35x + 14y) - (12x + 14y) = 91 - 22
⇒ 35x - 12x + 14y - 14y = 91 - 22
⇒ 23x = 69
⇒ 23x ÷ 23 = 69 ÷ 23
∴ x = 3

By substituting found value of x into (2),
⇒ 5(3) + 2y = 13
⇒ 15 + 2y = 13
⇒ 2y = 13 - 15
2y = -2
∴ y = -1

Thus the solution to the system is (3 , -1)