Question

Solve the system of equations algebraically 5x - 3y = 6 6x - 4y = 2

Answer 1

`x=9` and
`y=13`

Explanation:

We have been given a system of equations. We are asked to solve our given system algebraically.

`5x-3y=6...(1)`

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

From equation (1), we will get:

`x=(6+3y)/(5)`

Upon substituting this value in equation (2), we will get:

`6((6+3y)/(5))-4y=2`

`(36+18y)/(5)-4y=2`

`(36+18y)/(5)-(5*4y)/(5)=2`

`(36+18y-20y)/(5)=2`

`(36-2y)/(5)=2`

`(36-2y)/(5)*5=2*5`

`36-2y=10`

`36-36-2y=10-36`

`-2y=-26`

`(-2y)/(-2)=(-26)/(-2)`

`y=13`

Upon substituting
`y=13` in equation (1), we will get:

`5x-3(13)=6`

`5x-39=6`

`5x-39+39=6+39`

`5x=45`

`(5x)/(5)=(45)/(5)`

`x=9`