Question

How do you solve the system of equations `y- 4= 3( x + 2)` and `2x + 6y = 10`?

Answer 1

`x=-2.5`
`y=2.5`

Explanation:

1) `y-4=3(x+2)`

2) `2x+6y=10`

Solve for `y` in the first equation

`y=3(x+2)+4`
`color(white)y=3x+6+4`
`color(white)y=3x+10`

Substitute it in the second equation

`2x+6(3x+10)=10`
`2x+18x+60=10`
`20x+60=10`
`20x=-50`
`x=-50/20`
`color(white)x=-5/2`
`color(white)x=-2.5`

Substitute `x` in the one of the equations to find `y`

`2(-2.5)+6y=10`
`-5+6y=10`
`6y=15`
`y=15/6`
`color(white)y=5/2`
`color(white)y=2.5`