Question

How do you solve this system of equations: `4x = 3y - 5 and 3x + 3= 4y`?

Answer 1

Isolate variables and constants on different sides, add the equations together, solve for one variable in terms of the other, then use original equations to find the solution. `x=-11/7, y=-3/7`

Explanation:

It may behoove us to rewrite the equation in a more standard form, with the variables on one side and the constants on the other:

`4x=3y-5 -> 4x-3y=-5`
`3x+3=4y -> -3x+4y=3`

If we simply add these together, we obtain...

`(4x-3x) + (-3y+4y) = (-5+3) -> x+y = -2 -> y = -x -2`

We can substitute this into either of our initial equations...

`3x+3 = 4(-x-2) = -4x -8 -> 7x = -11 -> x = -11/7`

Then...

`y=-x-2 -> y = 11/7 -14/7 = -3/7`

Check...

`4x=3y-5 -> -44/7 = -9/7 - 35/7` correct

`3(-11/7) + 3 = 4(-3/7) -> -33/7 + 21/7 = -12/7` correct