Question

How do you solve the system 7r-2s=33 and 2r+7s=70?

Answer 1

The solutions are
`color(blue)(s=8,r=7`

Explanation:

`7r-2s=33`, multiplying by `2`
`color(blue)(14r)-4s=66`.....equation `1`

`2r+7s=70`, multiplying by `7`
`color(blue)( 14r)+49s=490`.....equation `2`

Solving by elimination
Subtracting equation `2` from `1`
`color(blue)(14r)-4s=66`
`cancelcolor(blue)( -14r)-49s=-490`

`-53s=-424`
`color(blue)(s=8`

Finding `r` from equation `1`
`7r-2s=33`
`7r=33+2s`
`7r=33+16`
`7r=49`
`color(blue)(r=7`