Question

How do you solve 4x + 5y = 1 and 7y - 3x = 2?

Answer 1

`x=-3/43`
`y=11/43`

Explanation:

There are two ways you can solve this: substitution or elimination. I'll go with substitution since I personally like it better.

Let's try looking for the value of `x` first. We'll first try to isolate `y` in the first equation.
`4x+5y=1`
`5y=1-4x`
`y=(1-4x)/5`

Now we will substitute this value of `y` to the second equation.
`7y-3x=2`
`7((1-4x)/5)-3x=2`
(We'll multiply both sides by 5 to remove the denominator)
`(5)[7((1-4x)/5)-3x]=(5)(2)`
`7(1-4x)-15x=10`
`7-28x-15x=10`
`7-43x=10`
`-43x=10-7`
`-43x=3`
`x=-3/43`

To solve for `y`, substitute the value of `x` we just got into either of the two equations.
`4x+5y=1`
`4(-3/43)+5y=1`
`-12/43+5y=1`
`5y=1+12/43`
`5y=43/43+12/43`
`5y=55/43`
`(1/5)5y=(1/5)55/43`
`y=11/43`