Question

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

Answer 1

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

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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

Answer 2

Answer:

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

Step-by-step 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:

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

$x^2+25x^2=26$

$26x^2=26$

$\frac{26x^2}{26}=\frac{26}{26}$

$x^2=1$

$x=\pm \sqrt{1}$

$x=\pm 1$

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 $(1,5)$.