Show how to use substitution or elimination to solve the following system of equations. Write the solution as an ordered pair.
4x-y=10
Y=2x-2

  (4, 6)

Step-by-step explanation:

Substitution

Using the second equation, we can substitute for y in the first equation.

  4x -(2x-2) = 10

  2x +2 = 10 . . . . simplify

  x +1 = 5 . . . . . . .divide by 2

  x = 4 . . . . . . . . . subtract 1

  y = 2(4) -2) = 6 . . . . substitute for x in the equation for y

The solution is (x, y) = (4, 6).

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Elimination

Often, we like to start with both equations in standard form when we solve by elimination. That is nice, but not completely necessary.

We can eliminate the y-variable by simply adding the two given equations.

  (4x -y) +(y) = (10) +(2x -2)

  4x = 8 + 2x . . . . . collect terms. The y-variable has been eliminated.

  2x = 8 . . . . . . . . . subtract 2x

  x = 4 . . . . . . . . . . divide by 2

Y can be found using the second equation.

  (x, y) = (4, 6)

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We could have eliminated the x-variable by multiplying the second equation by 2, then adding the two equations.

  (4x -y) +2(y) = (10) +2(2x -2)

  y = 6 . . . . . . . . . subtract 4x from both sides. The x-variable has been eliminated.

Now, x can be found using either equation.

  6 = 2x -2 . . . substitute for y in the second equation

  3 = x - 1 . . . divide by 2

  x = 4 . . . . . add 1

  (x, y) = (4, 6)