Question

How do you find the solution of the system of equations `x + y = -7` and `3x + y = -9`?

Answer 1

Solving by elimination and substitution:

`x+y = -7`............................equation 1
`3x + y = -9`.........................equation 2

multiplying equation 1 by `-1` for elimination we get:
`-x -y = 7`

on adding the two equations `y` gets cancelled
`-x -cancel(y) = 7`
`3x + cancel(y) = -9`

`2x = -2`

`x = -2/2 = -1`

substituting this value of `x` in equation 1:
`x+y = -7`
`-1 + y = -7`
`y = -7 + 1`

`y = -6`

the solution for the system of equations is:
`color(blue)x=-1`
`color(blue)y=-6`