Will give ! what is the solution to the system of equations using the linear combination method? 3x+y=4 2x+y=7 (−1, 7) (−3, 13) (−3, 12) (0, 4)

Mark the two equations below as A and B,

A: 3x+y=4

B: 2x+y=7

Because there's a y for both A and B, elimination (or linear combination, depending on the book) works well. If we add both equations we get 2y for the y terms. What if we subtracted instead. y - y = 0, and we eliminate the y terms. For subtracting, we multiply B by -1.

3x + y = 4

-2x - y = -7

Adding both equations (remember to change the signs on B) gives that 1x = -3 and so x = -3.

Now we take x = -3 and put into an original equation. Let's go into A.

3x+y=4

3 * -3 + y = 4 letting x = -3

-9 + y = 4

y = 13 adding 9 on both sides

So x = -3 and y = 13, or the ordered pair (-3, 13) - the 2nd one given - is our solution.

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