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Use the elimination method to solve each system. …

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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 22 Medium Difficulty

Use the elimination method to solve each system.
$$
\left\{\begin{array}{l}
{x+7 y=-22} \\
{x+9 y=-24}
\end{array}\right.
$$

Answer

$y=-1$

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Algebra

Elementary and Intermediate Algebra

Chapter 4

Systems of Linear Equations and Inequalities

Section 3

Solving Systems of Equations by Elimination (Addition)

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Equations and Inequalities

Systems of Equations and Inequalities

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Video Transcript

to solve the system of equations by elimination. We want to have opposite coefficients on X or opposite coefficients on Why and I'm going to go for opposite coefficients on X. I'm going to label the first equation one and the second equation, too. So to get opposite coefficients on X, I'm going to multiply equation one by negative one. And now Equation one is the opposite of X minus seven y equals 22 and I'm going to leave equation to unchanged, so it's still X plus nine y equals negative 24. Now, when we add these equations together, the ex terms are eliminated and we have to. Why equals negative, too, to by both sides by two. And we have y equals negative one. Now to find the X value, we can substitute that. Why value into equation one or equation to it doesn't matter which. So I'm going to choose equation one, and we have X plus seven times. Negative one equals negative 22. So that would be X minus seven equals negative 20 to add seven to both sides and we have X equals negative 15. And before I give my answer, I'm going to check to make sure it's right by substituting both numbers into equation, too. By the way, this is my second time doing this problem because the first time I made a mistake and didn't realize it. And it was when I checked it that I found my mistake. So I tell you that because the check is really important. Okay, so now substituting these numbers into equation too negative 15 plus nine times negative one is negative. 24. So that's negative. 15 plus negative nine is negative. 24. And that checks. So our answer is correct. We can write it as an ordered pair X comma y negative 15 common negative one.

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Alan S. Tussy, R. David Gustafson

Elementary and Intermediate Algebra

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