Question

Solve the system of linear equations by substitution. Check your solution.

Answer 1

`x = 1.5`

`y =1`

Explanation:

Given

`4x + 2y = 8`

`6x - 4y = 5`

Required

Solve for x and y

`4x + 2y = 8` --- (1)

`6x - 4y = 5` --- (2)

Divide equation (1) through by 2

`(1)/(2)(4x + 2y) = 8*(1)/(2)`

`2x + y = 4`

Make y the subject

`y = 4 - 2x`

Substitute 4 - 2x for y in equation (2)

`6x - 4y = 5`

`6x - 4(4- 2x) = 5`

Open bracket

`6x - 16+ 8x = 5`

Collect Like Terms

`6x + 8x = 5+16`

`14x = 21`

Solve for x

`x = (21)/(14)`

`x = 1.5`

Substitute 1.5 for x in
`y = 4 - 2x`

`y = 4 - 2(1.5)`

`y = 4 - 3`

`y =1`

To check the solution:

Substitute the values of x and y i the equations

`4x + 2y = 8`

`4 * 1.5 + 2 * 1 = 8`

`8 = 8`

`6x - 4y = 5`

`6 * 1.5 - 4 * 1 = 5`

`5 = 5`

Hence, the solution is true