Question

Solve algebraically the simultaneous equation
x^2=y^2=25
y=2x-2

Answer 1

Answer: (3,4) and (-7/5, -24/5)

Explanation:

I presume that the first equation says
`x^2+y^2=25`

If so, we can sub y = 2x - 2 into the first equation to get

`x^2 + (2x-2)^2 = 25`

`x^2+4x^2-8x+4=25`

`5x^2-8x+4-25=0`

`5x^2-8x-21=0`

`(5x+7)(x-3)=0`

`x = 3` or
`-7/5`

Sub the values into y to get

`y = 2(3)-2 = 4` or
`y = 2(-7/5)-2=-24/5`