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Use the elimination method to solve each system.$$\left\{\begin{array}{l}{\frac{1}{8} x-\frac{1}{8} y=\frac{3}{8}} \\{\frac{x}{4}+\frac{y}{4}=\frac{1}{2}}\end{array}\right.$$
(2.5,-0.5)
Algebra
Chapter 4
Systems of Linear Equations and Inequalities
Section 3
Solving Systems of Equations by Elimination (Addition)
Equations and Inequalities
Systems of Equations and Inequalities
Harvey Mudd College
Baylor University
Idaho State University
Lectures
01:32
In mathematics, the absolu…
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Use the elimination method…
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Solve each system using th…
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Solve the system by either…
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to solve this system. The first thing I would do is clear the fractions. So in the first equation will multiply all of the terms by eight. And that gives us X minus y equals three and in the second equation will multiply all of the terms by four. And that gives us X plus y equals two. Now we have a system and notice that the white terms are opposites. And so if we add these equations together, the white terms will eliminate at the X terms and we get to X. And then we have the white terms eliminated and we add wth e coefficients, and we get five. Now we can divide both sides by two, and we get X equals five house. Now we want to find the value of why. So we're going to substitute our X value into one of our two equations. I'll call this equation one. We'll call this the equation, too. So suppose I substitute my ex value into equation, too. That means I will have five halves plus y equals two. I'll subtract five hats from both sides and I get why equals negative 1/2. So before we give our answer. Let's go ahead and check and make sure it's right by substituting both numbers into Equation one. So that would be five halves minus negative, 1/2 his three five halves minus negative. 1/2 is five halves plus 1/2 and that six halves and six halves is equal to three. So that checks. So our answer, written as an order pair X comma Y is five halves comma, negative 1/2.
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