Question

How do you solve the simultaneous equations `x²+y²=5` and `y=3x+1`?

Answer 1

`x = 2/5,quad y=11/5`

or

`x = -1, y=2`

Explanation:

Substitute `y=3x+1` in `x^2+y^2=5` to obtain

`x^2+(3x+1)^2=5qquad implies qquad 10x^2+6x-4=0`

Hence

`5x^2+3x-2 = 0 qquad implies qquad 5x^2+5x-2x-2 = 0qquad implies`
`5x(x+1)-2(x+1) = 0 qquad implies qquad (5x-2)(x+1) = 0`

Hence

• either `x= 2/5`, `y = 3times 2/5+1 = 11/5`
• or `x = -1`, `y = 3 times (-1)+1 = -2`