Question

Solve the following simultaneous equations: x/4 + y = 1 and (x-3)/2 = 2y

Answer 1

(x, y ) = (
`(7)/(2)`,
`(1)/(8)`)

Explanation:

given the 2 equations

`(x)/(4)` + y = 1 → (1)

`(x-3)/(2)` = 2y → (2)

multiply (1) by 4 and (2) by 2 to eliminate the fractions

x + 4y = 4 → (1)

x - 3 = 4y → (2)

rearrange (2 ) expressing x in terms of y

x = 4y + 3 → (3)

substitute x = 4y + 3 into (1)

4y + 3 + 4y = 4

8y + 3 = 4 ( subtract 3 from both sides )

8y = 1 ( divide both sides by 8 )

y =
`(1)/(8)`

substitute this value into (3 ) for x

x = (4 ×
`(1)/(8)`) + 3 =
`(7)/(2)`

solution is (
`(7)/(2)`,
`(1)/(8)`)