Question

How do you solve `2a + 3b = -1` and `3a + 5b = -2`?

Answer 1

The solutions are
`color(blue)(a=1,b=-1`

Explanation:

`2a+3b=−1`, multiplying the equation by `3`
`color(blue)(6a)+9b=−3`..........equation `1`

`3a+5b=−2`multiplying the equation by `2`
`color(blue)( 6a)+10b=−4`.......equation `2`

Solving by elimination .
Subtracting equation `2` form `1`

`cancel( color(blue)(6a))+9b=−3`
`cancel(-color(blue)( 6a))-10b=+4`

`-b=1`
`color(blue)(b=-1`

Substituting `b` in equation `1` to find `a`:
`2a+3b=−1`
`2a=−1-3b`
`2a=−1-3*(-1)`
`2a=2`
`color(blue)(a=1`