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Use the elimination method to solve each system.$$\left\{\begin{array}{l}{-9 x+5 y=-9} \\{-9 x-5 y=-9}\end{array}\right.$$
$x=1$$y=0$
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
Baylor University
Idaho State University
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Let's solve this system with the elimination method and notice that your why terms are opposites. We have five. Why? And we have negative five. Why? So when we add those two equations together, those will cancel. They'll eliminate. So we're gonna add the ex terms Negative. Nine X plus Negative. Nine X is negative. 18 x We eliminate the white terms because five white plus negative five y zero and then we have the Constance together. Negative nine plus negative nine is negative. 18. So we have negative 18. X equals negative. 18. Let's divide both sides of that equation by negative 18 and we get X equals one. Now we need to find why. And so we're going to substitute the one into one of our two equations. So I'm going to call this equation one. And this is equation, too, so I'll substitute into Equation one, which was negative. Nine. X plus five y equals negative. Nine. I'll put the one in there for X negative. Nine times one plus five y equals negative. Nine. So this is negative. Nine plus five y equals negative nine and nine to both sides, and we get five y equals zero divide both sides of that by five. When we have Y equals zero. Now, before we write our answer, let's go ahead and do a check. And the way to check is to substitute the numbers into the second equation. So that would be negative. Nine times one minus five times zero equals negative. Nine. That would be negative. Nine minus zero equals negative. Nine that checks. So we're good. So now we read her answer as an ordered pair x comma y one comma zero.
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