Question

How do you solve the following linear system: `4x+3y=8 , x-2y=13`?

Answer 1

`(x,y)=(5,-4)`

Explanation:

`4x+3y=8`

`x-2y=13`

In the second equation we can find the value of `x` by transposing `2y` to the other side of the equation and we can substitute the value of `x` to the other equation

Solve for second equation:

`rarrx-2y=13`

Add `2y` both sides:

`rarrx=13+2y`

Substitute the value of `x` to the first equation:

`rarr4(13+2y)+3y=8`

`rarr(52+8y)+3y=8`

`rarr52+8y+3y=8`

`rarr52+11y=8`

`rarr11y=8-52`

`rarr11y=-44`

`rarry=-44/11=-4`

So,substitute value of y to second equation:

`rarrx-2(-4)=13`

`rarrx-(-8)=13`

`rarrx+8=13`

`rarrx=13-8=5`

So,`(x,y)=(5,-4)`