Question

Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10? Select two options.

y = x2 + 5x + 10
y + 5x = x2 + 10 + 4x – 10
0 = x2 – 9x
0 = x2 – 9x + 20
One x-value of a solution to the system is 4.

Answer 1

D - 0+x^2-9x+20

E - One x-value of a solution to the system is 4

Explanation:

Answer 2

That would be :

4x – 10 = x2 – 5x + 10 ( y = 4x - 10 is substitute for y)

PROOF: y + 5x = x² + 10

(4x - 10) + 5x = x² + 10

4x - 10 = x² -5x + 10

0 = x2 – 9x + 20 (liked terms are grouped and simplified)

PROOF: 4x - 10 = x² -5x + 10

4x = x² -5x + 10 + 10

0 = x² -5x -4x + 20

0 = x² - 9x + 20

Solving:

x² - 9x + 20 = 0

x² - 5x - 4x + 20 = 0

(x - 5) (x - 4) = 0

⇒ x = 4 (as question says) OR x = 5

Explanation:

hope this helps