Solve each system by elimination. In systems with fractions, firs...

Question

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2.
5x + 7y = 6 
10x - 3y = 46

Accepted Answer

Everybody everything. All right today that we're going to be looking at this question that states using the elimination method, solve the following system of equations where our system of equations will include equation number one as four, X plus Y equals 13. And equation number two will be three, X minus five, Y equals four. Now the answers provided are A X equals one and Y equals three B X equals three and Y equals one, C X equals five and Y equals four and D X equals four and Y equals five. Now for a question like this where they tell us to use the elimination method. What we're going to be trying to doing to do is see how we can manipulate our system of equations in a way that when we add them up, one of the variables will be eliminated. So what we'll do in this case is I'm going to multiply equation number one by five. So how five multiplying an open bracket or X plus Y equals 13 close bracket? So we're also multiplying the 13 by the five and equation number two will stay the same. So we'll have five multiplied by four, X will be 20 X five multiplied by Y will be five Y. So we have 20 X plus five Y and then we'll have five multiplied by the 13. So we'll have 20 X plus five, Y equals five multiplied by 13, which is 65. And that will be our new equation number one. And under that equation number one, I'll put, I'll write equation number two, which is three, X minus five, Y equals four. And I write them one on top of the other because this will help us visualize adding them up. So usually when we're taught how to do addition, they always sell us to put the numbers one on top of the other, write the addition symbol and write the line and add them up. So if we write each equation on top of the other, we can do the same thing. We write the audition symbol, write the line and just add them up. So we'll have that 23 X or 20 X plus three. X is 23 X. We have five, Y minus five, Y is zero. So we eliminated the Y. So we'll have 23 X is equal to 65 plus four, which is 69. And then if we divide both sides by 23 we'll have that X is equal to three. So that'll be our value for X and all we did was eliminate. So using the elimination method, we eliminated the variable Y and solve for X. And now we can use that X to plug it into equation one. So we'll have four multiplied by X, which is three. So we have 44, multiplied by three plus Y equals 13, four, multiplied by three is 12. So we have 12 plus Y equals 13. And then we just move the 12 over from the left hand side to the right hand side by subtracting and 13 minus 12 is one. So that means that our Y is equal to one. So answer choice B has X equals three and Y equals one, which is the answer to our question. So I hope that was helpful. And until next time.

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 5x + 7y = 6 10x - 3y = 46

Key Concepts

Systems of Equations

Elimination Method

Clearing Denominators

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