Question

How do you solve the system of equations `2x + 3y = 13` and `3x - 5y = - 9`?

Answer 1

#(x,y)=(2,3)

Explanation:

`2x=13-3y`
`x=13/2-3/2y` solve for `x` in terms of `y` in the first equation
`3(13/2-3/2y)-5y=-9` plug into the other equation
`39/2-9/2y-10/2y=-18/2` distribute and set a common denominator
`39/2-19/2y=-18/2`
`39-19y=-18` this is a matter of personal preference, but I like to multiply the whole equation by the denominator to get rid of fractions (for now)
`-19y=-57`
`y=57/19`
`y=3`

Now, going back to the other equation
`2x+3(57/19)=13` plug in value of y
`2x+171/19=13`
`2x+9=13`
`2x=4`
`x=2`