Question

How do you solve `x^2+y^2=25, 4x+3y=0`?

Answer 1

`(-3, 4) and (3, -4)`

Explanation:

`x^2+y^2=25`
`4x+3y=0` => solve for y in terms of x:
`3y=-4x`
`y=(-4x)/3` => substitute in the first equation:
`x^2+[(-4x)/3]^2=25`
`x^2 +(16x^2)/9=25` => multiply all terms by 9:
`9x^2+16x^2=25*9`
`25x^2=25*9`
`x^2=9` => solve for x:
`x=+-3`
`x=-3, y=4`
`x=3, y=-4`
What we have is a straight line(2nd equation) that intercepts a circle(1st equation) in the above points(the solutions)