Question

What is the solution of this system of linear equations?

3y = 3 y equals StartFraction 3 over 2 EndFraction x plus 6.x + 6
y – StartFraction one-half EndFraction y minus StartFraction 1 over 4 EndFraction x equals 3.x = 3

Answer 1

C. no solution

Explanation:

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Answer 2

`x = 4`

`y = 4`

Explanation:

Given

`3y = (3)/(2)x + 6`

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

Required

The solution

Multiply the second equation by 3

`3 * [y-(1)/(4)x = 3]`

`3y-(3)/(4)x = 9`

Rewrite as:

`3y =(3)/(4)x + 9`

Subtract this from the first equation

`[3y = (3)/(2)x + 6]- [3y =(3)/(4)x + 9]`

`3y - 3y = (3)/(2)x - (3)/(4)x + 6 - 9`

`0 = (3)/(4)x -3`

Rewrite as:

`(3)/(4)x =3`

Multiply both sides by 3/4

`x =3*(4)/(3)`

`x = 4`

Substitute
`x = 4` in
`3y = (3)/(2)x + 6`

`3y = (3)/(2) * 4 + 6`

`3y = 6 + 6`

`3y = 12`

Divide both sides by 3

`y = 4`