Question

What are the solutions to the nonlinear system of equations below?. y = 5x, x2 + y2 = 26

Answer 1

`x=\pm 1,y=\pm 5`

Explanation:

We have been given a nonlinear system of equations. We are asked to find the solution for our given nonlinear system of equations.

`y=5x...(1)`

`x^2+y^2=26...(2)`

To solve our given system, we will use substitution method.

Upon substituting equation (1) in equation (2), we will get:

`x^2+(5x)^2=26`

`x^2+25x^2=26`

`26x^2=26`

`(26x^2)/(26)=(26)/(26)`

`x^2=1`

`x=\pm √(1)`

`x=\pm 1`

To find value of y, we will substitute
`x=-1` in equation (1).

`y=5(-1)`

`y=-5`

Therefore, one solution for our given system is
`(-1,-5)`.

To find second value of y, we will substitute
`x=1` in equation (1).

`y=5(1)`

`y=5`

Therefore, one solution for our given system is
`(1,5)`.

Answer 2

Solutions are (1, 5) and (-1, -5).

_____
If you're interested, you can make the substitution for y and solve the resulting quadratic in x. I find a graphing calculator to be handy for these.

x^2 +(5x)^2 = 26
26x^2 = 26
x = ±1