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 2.2x - 3y = -7 5x + 4y = 17

Accepted Answer

Hey, everyone. Here we are asked to use the elimination method to solve the following system of equations where the first given equation is three, X minus five, Y is equal to negative two. And the second equation is four, X plus two, Y is equal to six. Here we have four answer choice options. Answer choice A X and Y are equal to negative one answer B X is equal to one and Y is equal to negative one answer choice C X is equal to negative one and Y is equal to one and answer D X and Y are equal to one. So here to utilize the elimination method, we first need to select one of the variables that we want to solve for first. So here we can choose to just solve for X first. And so that means we need to manipulate both of the equations such that our Y terms are the same aside from their side. So we can start by multiplying our first equation, the left side and the right side by two. And so this gives us a new equation of six, X minus 10 Y is equal to negative four. And for our second equation again, we want the same Y terms or the same coefficients aside from the sign. So we will multiply the left side and the right side of the second equation by five. And so this gives us a second equation of 20 X plus 10 Y is equal to 30. So now we see here that our Y terms have the same coefficients but their signs are opposite. So this means that we need to add both equations together so that our Y terms cancel out. So beginning with our X terms, we have six X plus 20 X which gives us X. Then with our Y terms, we see we have negative 10, Y plus 10 Y which cancels to zero as we wanted. And then on the right side of the equations, we have negative four plus 30. So our expression is equal to 26. So from adding our two equations together, we get a new equation of 26 X is equal to 26. Now just solving for X, we divide both sides by 26 we see our value for X is just one. And so now we have found our value for one. So we now need to find the value for Y. So going back to the original system of equations again, we had three, X minus five, Y is equal to negative two and we also had four X plus two, Y is equal to six. So now again, we need to solve four Y. So we need need to get both of our X terms to be the same. So that means we will just multiply our first equation, the left side and the right side by four. And so this gives us a new equation of 12 X minus 20 Y is equal to negative A. And now for our second equation again, to get now the X terms to be the same, we will multiply the left side and the right side of the second equation by negative three. And so this gives us a new second equation of negative 12, X minus six Y is equal to negative 18. And so now again, we see our X terms have the same coefficient but different signs. So we just need to add the equation regions together. And so we have 12 X plus negative 12 X which is zero. And then we have negative 20 Y plus negative six Y which gives us minus 26 Y. And then we have on the right side negative eight plus negative 18. So our expression is equal to negative 26. So now we have our new equation here from adding our two equations together as negative 26 Y is equal to negative 26. So now just solving for Y, we divide both sides by negative 26. And so we get that our value for Y is the same as X as positive one. So now we have found our values for X and Y. So we are left here with answer choice D where X is equal to one and Y is also equal to one. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2.2x - 3y = -7 5x + 4y = 17

Key Concepts

Systems of Equations

Elimination Method

Clearing Denominators

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