Question

How do you find the solution of the system of equations `5x + 4y = 6` and `-2x - 3y = -1`?

Answer 1

Through elimination, we get:
`x=2`
`y=-1`

Explanation:

Manipulate the equations so that you can eliminate one of the variables. One possibility is to multiply the first equation by 2, and multiply the second equation by 5:

`+10x+8y=12`
`-10x-15y=-5`

Then add the two equations together to eliminate `x` and solve for `y`:
`0-7y=7`
`y=-1`

Now substitute the value of `y` into either of the original equations to find `x`:
`5x+4y=6`
`5x+4(-1)=6`
`5x = 6+4=10`
`x=2`