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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.

Sagot :

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.

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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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