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Solve the system by either the substitution or the elimination method.$$\left\{\begin{array}{l}{8 x+12 y=-22} \\{3 x-2 y=8}\end{array}\right.$$
$\left(1,-\frac{5}{2}\right)$
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
Campbell University
Harvey Mudd College
Baylor University
Idaho State University
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I'm going to use the elimination method to solve this system. And if I want to eliminate why, I could multiply the second equation by six. That way, the first equation has a 12 y, and the second equation has a negative 12 y. So rewriting these equations we have for our second equation 18 x minus 12 y equals 48. Now we can add the equations together. Eight x plus 18 x is 26 x The white terms have been eliminated and negative 22 plus 48 is 26. And that worked out perfectly. So X equals one now to find the value of why I'm gonna go back and label my original equations one and two and use either equation one or two. Whichever one you want to find. Why I'll just use the equation. One. So now I have eight times x. So eight times one plus 12 times why equals negative 22. So that's eight plus 12. Why equals negative? 22. We can subtract eight from both sides and we get 12 y equals negative. 30. Divide both sides by 12. We have negative. 30 over 12. That's not the nicest answer ever, but we can reduce it to negative five halves Now. We ought to check our answer to make sure that's actually right. So let's use the other equation equation to substitute our numbers in there. And we have three times one minus two times why two jumps negative. Five halves equals eight three times. One is three native, two times native. Five halves is five. So that did work out to eight. So that checks good. So now we write our answer as an ordered pair X comma y one common negative five hats.
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