Question

How do you solve the following system?: `-x+5y=7 , x=-2y+1`

Answer 1

Use linear combination or substitution.

Explanation:

Add the two equations together.
`-x+5y=7`
`+(x+2y=1)`
`color(red)(0x+7y=8)`
Therefore, `7y=8` and `y=8/7`. From here, plug `8/7` in for `y` in either equation and solve for `x`.

Another option would be substitution, since from the second equation you know that `x=-2y+1`, would be to replace `x` with `-2y+1` in the equation `-x+5y=7`.

This would give: `-(-2y+1)+5y=7`
`2y-1+5y=7`
`7y-1+7`
`7y=8`
Again, we see that `color(blue)(y=8/7)` and we would use that value to determine that `color(blue)(x=-9/7)`.