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Use the elimination method to solve each system. …

02:38

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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83 Problem 84 Problem 85 Problem 86 Problem 87 Problem 88 Problem 89 Problem 90 Problem 91 Problem 92 Problem 93 Problem 94 Problem 95 Problem 96 Problem 97 Problem 98 Problem 99 Problem 100 Problem 101 Problem 102 Problem 103 Problem 104

Problem 24 Medium Difficulty

Use the elimination method to solve each system.
$$
\left\{\begin{array}{l}
{6 x-y=4} \\
{9 x-y=10}
\end{array}\right.
$$

Answer

$x=2$
$y=8$

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Chapter 4

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Section 3

Solving Systems of Equations by Elimination (Addition)

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Video Transcript

all right, I'm going to start by labeling my equations one and two. And to solve the system with the elimination method, we need to have opposite coefficients on X or opposite coefficients on why and write down. Right now, we don't have either one. So if we multiply equation one by negative one, we will have opposite coefficients on why. So that gives us negative six x plus y equals negative for, and we'll leave the equation to unchanged, and that will be nine x minus y equals 10. So now we can add those equations together. Add the ex terms together and you get three X. The white terms are eliminated. And then add the Constance together and we get six. Divide both sides of that equation by three, and we get X equals two. Now we want to find the value of why. So we take that X value and we substitute it into one of the two equations. It doesn't matter which one, so I'm going to use equation one. So I have six times X so sixpence to minus y equals four. So that's 12 minus y equals four. Subtract 12 from both sides and we get the opposite y equals negative eight. So why equals eight? Now let's check our answer by substituting both numbers into equation, too. So that would be nine times two. Minus eight equals 10. So 18 minus eight equals 10 and that checks 10 equals 10. So then we write her answer as an ordered pair x comma y two comma eight.

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Alan S. Tussy, R. David Gustafson

Elementary and Intermediate Algebra

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