Question

How do you solve 6x-2y= - 3 and 5x+3y=4?

Answer 1

`color(blue)(x=-1/28`

`color(blue)(y=13/6`

Explanation:

`6x-2y=-3`, multiplying this equation by `3`

`18x-color(blue)(6y)=-9`.....equation `(1)`

`5x+3y=4`, multiplying this equation by`2`

`10x+color(blue)(6y)=8`.......equation `(2)`

Solving by elimination.
Adding equation `1` and `2` to eliminate `color(blue)(6y`

`18x-cancelcolor(blue)(6y)=-9`
`10x+cancelcolor(blue)(6y)=8`

`28x=-1`

`color(blue)(x=-1/28`

Finding `y` by substituting `x` in equation `1`

`18x-6y=-9`

`18x +9=6y`

`18*(-1/28) +9=6y`

`-9/14 +9=6y`

`(-9 +126)/9=6y`

`(117)/9=6y`

`13=6y`

`color(blue)(y=13/6`