Question

How do you solve the simultaneous equations `x – 2y = 1` and `x^2 + y^2 = 29`?

Answer 1

I found:
`x=5`; `y=2`
`x=-23/5`;`y=-15/5`

Explanation:

We can try isolate `x` from the first equation:
`x=1+2y`
substitute into the second (for `x`):
`(color(red)(1+2y))^2+y^2=29`
`1+4y+4y^2+y^2=29`
`5y^2+4y-28=0`
solve for `y` (using the Quadratic Formula) gives you:
`y_(1,2)=(-4+-sqrt(16+560))/10=(-4+-24)/10`
you get two solutions:
`y_1=-28/10=-14/5`
`y_2=20/10=2`
Substituted back to find `x` you get:
if `y=2` then `x=1+4=5`
if `y=-15/5` then `x=1-2*14/5=-23/5`