Question

What is the solution to 2x-y=10 and y=-1/2x+5

Answer 1

(6, 2)

Explanation:

Given the 2 equations

2x - y = 10 → (1)

y =
`(1)/(2)` x + 5 → (2)

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

2x - (-
`(1)/(2)` x + 5) = 10

2x +
`(1)/(2)` x - 5 = 10

`(5)/(2)` x - 5 = 10 ( add 5 to both sides )

`(5)/(2)` x = 15

Multiply both sides by 2 and divide by 5

5x = 30 ⇒ x = 6

Substitute x = 6 into (1)

12 - y = 10 ( subtract 12 from both sides )

- y = - 2 ( multiply both sides by - 1 )

y = 2

Solution is (6, 2)