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)

Question

asked Jan 18, 2019 191k views

2 Answers

Atmocreations · Answer 1 · 2019-01-24T12:53:22+0000

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

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

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

y=3*1=3.

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

y=3*(-1)=-3.

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

Options (C) and (D) are CORRECT.