Question

Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10? Check all that apply.

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

Answer 1

Algebraically solving the system involves substituting the second equation y = 4x - 10 into the first, simplifying to get a quadratic equation, and then setting it to zero to facilitate the use of factoring or the quadratic formula.

Step-by-step explanation:

When algebraically solving the system of equations given by y + 5x = x2 + 10 and y = 4x − 10, certain steps are part of the process. First, you would substitute the second equation into the first to eliminate the variable y. This is done by replacing y in the first equation with the expression on the right side of the second equation.

Therefore, the substitution step would be:

• y + 5x = x2 + 10
• 4x − 10 = y
• 4x − 10 + 5x = x2 + 10

After simplifying and reorganizing the terms, you arrive at a quadratic equation:

• 0 = x2 − 9x + 20

Therefore, the steps that could be part of this algebraic process include:

• Substituting 4x − 10 into y + 5x = x2 + 10, which gives us 4x − 10 = x2 − 5x + 10, after simplifying.
• Setting the equation to zero on the left side to prepare for factoring or applying the quadratic formula, resulting in 0 = x2 − 9x + 20.

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