Question

What is the solution of the following system of equations by 3x-2y=12 6x-4y=24

Answer 1

Infinitely many solutions.

Explanation:

Given

`3x-2y=12\\ 6x-4y=24`

Required;

Find the solution

`3x-2y=12 --(1)\\ 6x-4y=24 -- (2)`

Make x the subject of formula in (1)

`3x-2y=12`

Add 2y to both sides

`3x-2y+2y=12+2y`

`3x=12+2y`

Divide both sides by 3

`(3x)/(3)=(12+2y)/(3)`

`x=(12+2y)/(3)`

Substitute
`x=(12+2y)/(3)` in (2)

`6x-4y=24`

`6((12+2y)/(3))-4y=24`

`2(12+2y)-4y=24`

Open Bracket

`24+4y-4y=24`

`24+4y-4y=24`

Collect Like Terms

`4y-4y=24-24`

`0 = 0`

Based on the result above, the two equations have infinitely many solutions.