Question

question 16 of 25
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. ((-1, -3))
c. ((3, -1))
d. ((1, 3))
e. ((-3, 1))
f. ((10, -3))

Explanation:

Step1: Substitute $y=3x$ into the second equation

Substitute $y=3x$ into $x^2+y^2=10$:
$x^2+(3x)^2=10$

Step2: Simplify and solve for $x$

Expand and combine like terms:
$x^2+9x^2=10$
$10x^2=10$
$x^2=1$
$x=1$ or $x=-1$

Step3: Find corresponding $y$ values

For $x=1$: $y=3(1)=3$
For $x=-1$: $y=3(-1)=-3$

Step4: Match to options

Check which options match $(1,3)$ and $(-1,-3)$

Answer:

B. (-1, -3), D. (1, 3)