Question

How do you find the point of intersection for `x+2y=3` and `3x-y= -5`?

Answer 1

You use one equation to express one of the variables in terms of the other. Then you substitute that in the other equation.

Explanation:

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

Then:
`x+2*(3x+5)=3->7x+10=3->x=-1`

From the first equation:
`y=3x+5=3*(-1)+5=2`

So the intersection point is `(-1,2)`

Check your answer with the original equations!
`-1+2*2=3and3*(-1)-2=-5`