Question

What are the solutions to the nonlinear system of equations below? Check all that apply.

y=3x
x^2+y^2=10

A. (10,3)
B. (10,-3)
C. (1,3)
D. (-1,-3)
E. (-3,1)
F. (3,-1)

Answer 1

x= +or-1
y = + or - 3
The 2 solutions are
-(1,-3)
(1,3)

Answer 2

Answer:  the correct options are

(C) (1, 3)

(D) (-1, -3).

Step-by-step explanation:  We are given to solve the following non-linear system of equations :

$y=3x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x^2+y^2=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting the value of y from equation (i) in equation (ii), we get

$x^2+(3x)^2=10\\\\\Rightarrow x^2+9x^2=10\\\\\Rightarrow 10x^2=10\\\\\Rightarrow x^2=1\\\\\Rightarrow x=\pm\sqrt{1}\\\\\Rightarrow x=1,~-1.$

When x = 1, the from equation (i), we get

$y=3\times1=3.$

When x = -1, then from equation (i), we get

$y=3\times(-1)=-3.$

Thus, the required set of solutions are (1, 3) and (-1, -3).

Options (C) and (D) are CORRECT.