Question

Question 21 of 40

Solve the system of equations.
y = 3x
y=x² - 10
O O O O
A. (-2,-6) and (-5, -15)
OB. (2,6) and (5, 15)
C. (-2,-6) and (5, 15)
O D. (2,6) and (-5, -15)

Answer 1

C. (-2, -6) and (5,15)

Explanation:

Pre-Solving

We are given the following system of equations:

y=3x

y=x²-10

We can use substitution to solve this system.

Solving

Since both equations equal y, we can set them equal to each other due to transitivity.

We get:

3x = x² - 10

Subtract 3x from both sides.

x² - 3x - 10 = 0

We can factor this.

(x-5)(x+2)=0

x - 5 = 0

x = 5

x+2=0

x = - 2

So, x is either 5 or -2.

Substitute 5 as x in y = 3x.

We get:

y=3(5) = 15

So (5,15) is one solution.

Since x is also -2:

Substitute -2 as x in y = 3x.

We get:

y = 3(-2) = -6

So, the other solution is (-2, -6).

The answer is C.