Question

How do you solve the following linear system: `3x-2y=7, 3x+4y=12`?

Answer 1

The solution for the system of equations is :
`color(blue)(y=5/6`

`color(blue)(x=(26)/(9)`

Explanation:

`color(blue)(3x)−2y=7`......equation `1`
`color(blue)(3x)+4y=12`......equation `2`

We can solve the system of equations by elimination

By subtracting equation `2` from `1` we can eliminate `color(blue)(3x`

`cancelcolor(blue)(3x)−2y=7`
`-cancelcolor(blue)(3x)-4y=-12`

`-6y=-5`

`y=(-5)/(-6)`

`color(blue)(y=5/6`

Now we substitute this value of `y` in equation `1` to find `x`:

`3x−2y=7`

`3x=7+2y`

`3x=7+cancel2*color(blue)(5/cancel6`

`3x=7+5/3`

`3x=(21+5)/3`

`3x=(26)/3`

`x=(26)/(3*3)`

`color(blue)(x=(26)/(9)`