Question

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

Answer 1

The solution for the system of equations is
`color(blue)(x=5,y=-4`

Explanation:

`x-2y=13`

`x=color(blue)(13+2y`.....equation `1`

`4x+3y=8`.....equation `2`

Solving by substitution :

Substituting equation `1` in equation `2` to find `y`

`4x+3y=8`

`4*(color(blue)(13+2y))+3y=8`

`4*(color(blue)(13) ) + 4 *color(blue)((2y))+3y=8`

`52+8y+3y=8`

`52+11y=8`

`11y=8-52`

`11y=-44`

`y=(-44)/11`

`color(blue)(y=-4`

Now, we substitute this value of `y` in equation `1` to find `x`
`x=13+2y`

`x=13+2*color(blue)((-4)`

`x=13-8`

`color(blue)(x=5`