Question

What is the value of x in the solution to this system of equations?

5x−5y=120

y=−7x+8

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x =

Answer 1

x = 4

Explanation:

You want the value of x in the solution to the system of equations ...

• 5x -5y = 120
• y = -7x +8

Substitution

Since we have an expression for y, we can substitute for y in the first equation:

5x -5(-7x +8) = 120 . . . . . . . . use -7x+8 for y

5x +35x -40 = 120 . . . . . . eliminate parentheses

40x = 160 . . . . . . . . . . . add 40, collect terms

x = 4 . . . . . . . . . . . . . divide by 40

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Additional comment

Then the value of y is ...

y = -7(4) +8 = -28 +8 . . . . . substitute for x in the second equation

y = -20