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The step that is the part of the process of algebraically solving the given system of equations is (C) 4x – 10 = x2 – 5x + 10 and (E) 0 = x2 – 9x + 20.
What is an equation?
- An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =.
To find the step that is the part of the process of algebraically solving the given system of equations:
That would be:
(C) 4x – 10 = x2 – 5x + 10 ( y = 4x - 10 is substituted for y).
Proof:
- y + 5x = x² + 10
- (4x - 10) + 5x = x² + 10
- 4x - 10 = x² -5x + 10
(E) 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
Therefore, the step that is part of the process of algebraically solving the given system of equations is (C) 4x – 10 = x2 – 5x + 10.
Know more about equations here:
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The complete question is given below:
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.
(A) y = x2 + 5x + 10
(B) y + 5x = x2 + 10 + 4x – 10
(C) 4x – 10 = x2 – 5x + 10
(D) 0 = x2 – 9x
(E) 0 = x2 – 9x + 20
(F) One x-value of a solution to the system is 4.
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