Question

Solve the system of linear equations below, using substitution method.

8x+9y=368x+9y=36
3x+4y=163x+4y=16

Answer 1

`x = 0`

`y=4`

Explanation:

Given

`8x + 9y = 36`

`3x + 4y = 16`

Required

Solve using substitution method

Make x the subject in
`3x + 4y = 16`

`3x = 16 - 4y`

Divide through by 3

`x = (1)/(3)(16 - 4y)`

Substitute
`(1)/(3)(16 - 4y)` for x in
`8x + 9y = 36`

`8*(1)/(3)(16 - 4y) + 9y = 36`

`(8)/(3)(16 - 4y) + 9y = 36`

Open bracket

`(8)/(3)*16 - (8)/(3)*4y + 9y = 36`

`(8*16)/(3) - (8*4y)/(3) + 9y = 36`

Multiply through by 3

`3 * (8*16)/(3) - 3 *(8*4y)/(3) +3* 9y = 36*3`

`8*16 - 8*4y +3* 9y = 36*3`

`128- 32y +27y = 108`

`128-5y = 108`

Collect Like Terms

`-5y = 108-128`

`-5y = -20`

Make y the subject

`y = (-20)/(-5)`

`y=4`

Substitute 4 for y in
`x = (1)/(3)(16 - 4y)`

`x = (1)/(3)(16 - 4*4)`

`x = (1)/(3)(16 - 16)`

`x = (1)/(3)(0)`

`x = 0`