SOLUTION: The directions say Use linear combinations to solve the system of linear equations. I tried to work this problem, but my teacher didn't go over it clearly. The problem is x-y=0 -

Question 123454This question is from textbook Algebra 1
: The directions say Use linear combinations to solve the system of linear equations. I tried to work this problem, but my teacher didn't go over it clearly. The problem is x-y=0 -3x-y=2. I don't know what to multiply so that the x or y value leaves the equation so i can solve it
This question is from textbook Algebra 1

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Linear combination is also known as Gaussian Elimination. The idea is to multiply one or both of the equations by some constant so that the coefficient on one of the variables is the additive inverse of the coefficient on the same variable in the other equation.

In the given system, you can set it up to eliminate x by multiplying the first equation by 3. That would give you 3x in the first equation and -3x in the second. You could also multiply either equation by -1. That would give you y in one equation and -y in the other.

Multiply the first equation by 3:

Now add the new equation to the second equation, term by term:

Next solve the resulting equation for the remaining variable:

Next, you can either substitute the value you just determined for y into either equation and solve for x, or you can repeat the elimination process to eliminate the y variable. Either way works.

If then so

or

Multiply the first equation by -1

Add the second equation to the new one:

Same answer.
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