Question

Which of the following ordered pairs are solutions to the system of equations below?

(3x + 5y = 14
y = 1/2x + 5)
O (2.4)
0 (-2,4)
O (2,6)
O (-2,6)

Answer 1

The answer should be B

Answer 2

(- 2, 4 )

Explanation:

Given the 2 equations

3x + 5y = 14 → (1)

y =
`(1)/(2)` x + 5 → (2)

Substitute y =
`(1)/(2)` x + 5 into (1)

3x + 5(
`(1)/(2)` x + 5) = 14

3x +
`(5)/(2)` x + 25 = 14

`(11)/(2)` x + 25 = 14 ( subtract 25 from both sides )

`(11)/(2)` x = - 11 ( multiply both sides by 2 )

11x = - 22 ( divide both sides by 11 )

x = - 2

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

y =
`(1)/(2)` × - 2 + 5 = - 1 + 5 = 4

solution is (- 2, 4 )