Use substitution to sole the system of equations

Question

asked Sep 6, 2024 112k views

1 Answer

Mpaton · Answer 1 · 2024-09-10T01:38:15+0000

Answer:

(0, 0)

(4, 16)

Explanation:

y = 4x

y = x^2

Using substitution, we can replace y in the second equation with 4x from the first equation.

4x = x^2

Now, we can move all the x's to one side and complete the square to solve for x.

0 = x^2 - 4x

↓ adding 4 to both sides

4 = x^2 - 4x + 4

↓ factoring the right side

4 = (x-2)^2

↓ taking the square root of both sides

$\sqrt4 = \sqrt{(x-2)^2$

$\pm2 = x - 2$

↓ adding 2 to both sides

$2 \pm 2 = x$

$\boxed{x = 0 \ \ \ \text{or} \ \ \ x = 4}$

Then, we can solve for y by plugging both x-values into the first equation.

y = 4(0) or
y = 4(4)

$\boxed{y = 0 \ \ \ \text{or} \ \ \ y=16}$

Finally, we can form two ordered pairs that are the solutions to the system of equations.

$\boxed{(0,0)}$

$\boxed{(4,16)}$