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Solve the system by either the substitution or the elimination method.$$\left\{\begin{array}{l}{4 x-7 y+32=0} \\{5 x=4 y-2}\end{array}\right.$$
$y=8$$x=6$
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
Missouri State University
Harvey Mudd College
Baylor University
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So in thinking about what method to use here, I think I would like to use the elimination method because I would like to avoid having a lot of fractions involved. But I need to convert the equations into standard form. So the first equation will subtract 32 from both sides, and we get four X minus seven y equals negative 32 and for the second equation will subtract four y from both sides. So we have five X minus four. Y equals negative, too. Now, if I multiply the top equation by five and the bottom equation by negative four, we'll have opposite ex terms and they will eliminate. So we have 20 x minus 35. Why equals negative 1 60 and we have negative 20 X plus 16? Why equals eight? So let's add those two equations together. We eliminate the ex terms. The white terms add to negative 19 Why? And the constants add to negative 1 52 Let's see what we get when we divide 1 52 by 19. Hopefully, it goes in nicely. We get eight. That's good. So divide both sides of this by negative 19 and we get y equals eight. And now for the value of X, I'm gonna go back to my original equations. My, uh, right over here one and two is what a label them. And I'm gonna use equation too. So I'm going to find the value of X by plugging eight infor. Why in equation too? So five X equals four times eight minus two. So five X equals 32 minus two 32. Minus two is 30. Divide both sides by five and we get six. Now. We should check our answer to make sure that everything worked out right before we finished. So I'll check with the equation Number one. So that would be for XO for 10 6 minus seven. Why, seven times eight plus 32? Equal zero. Let's see if that works. We get 24 minus 56 plus 32 equal zero, and that does check. So answer as an ordered pair. X comma Y is six comma eight
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