Question

How do you solve the following system?: `-3x +8y =-7 , 2x +2y = 4`

Answer 1

The 2nd equation really should be reduced to `x+y=2` and life become simpler,
Now we have the first equation as `-3x+8y=-7`.
Let us multiply everything in our simplified equation 2 by 3 so that we have the same coefficient but opposite sign , now our modified equation 2 becomes `3x+3y=6`
Note that we are not changing equation 2, they are all the same equation 2.

Since we have same coefficient and opposite sign, we can add the equations and eliminate the X variable to obtain `11y= -1`

This is great because now y becomes -1/11

Now we can substitute this y value into any of the equations , but preferably pick the simplest one, so that you have less chance of making a goofy error, so put it into X + y = 2 and you will get X = 23/11