What is the solution to the system of equations using the linear combination method?

We are given two equations as shown above. Call them A and B.

A: 5x + y = 2

B: 4x + y = 5

Both A and B have a y term. If you add the y terms you get 2y, which doesn't help. What does help is to subtract. Another name for the Linear Combination method is the Elimination Method - with the goal to Eliminate one of the variables.

5x + y = 2

4x + y = 5

Now we multiply equation B by -1 so that we can subtract.

5x + y = 2

-4x - y = -5

We add the two new equations together.

1x = -3

So x = -3. Now we take x = -3 and put it back into an original equation. Choose B.

4x + y = 5

4(-3) + y = 5 putting in x = -3

-12 + y = 5 multiplying the -3

y = 17 adding 12 to both sides

Our solution is x = -3, y = 17, or the ordered pair (-3, 17).

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step-by-step explanation:

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