Problem

Use the elimination method to solve each system. …

02:16

Problem 35 Hard Difficulty

Use the elimination method to solve each system.
$$
\left\{\begin{array}{l}
{\frac{3}{4} x-\frac{5}{8} y=\frac{1}{24}} \\
{\frac{5 x}{6}-y=\frac{1}{4}}
\end{array}\right.
$$

Answer

$(-0.5,-2 / 3)$

Related Courses

Algebra

Elementary and Intermediate Algebra

Chapter 4

Systems of Linear Equations and Inequalities

Section 3

Solving Systems of Equations by Elimination (Addition)

Discussion

You must be signed in to discuss.

Top Algebra Educators

Watch More Solved Questions in Chapter 4

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

Video Transcript

to solve this system, I would start by clearing the fractions so I would multiply the first equation by 24 and multiply the second equation by 12. So for the first equation that gives us so 3/4 times 24 18 so 18 X minus and 5/8 times 24 is 15. So minus 15 y equals one. And for the second equation 56 times 12 is tense. We get 10 y 10 X minus 12 y equals three. Okay, Next what we want to do is find a way to get opposite coefficients on X or why, so that we can eliminate one of them. So we need to find the least common multiple of 18 and 10 or the least common multiple of 15 and 12. I think I'm just gonna go for the least common multiple of 15 and 12 which is 60. And so I need to multiply the first equation by four to get negative 60. Why? And multiply the second equation by negative five to get positive. 60 way. Okay, so the first equation, when we multiply everything by four, we get 72 x minus 60 y equals four and the second equation. When we multiply everything by negative five, we get negative. 50 X plus 60. Why equals negative? 15. Now we're gonna add those two equations together, and that gives us 22 x the Y terms eliminate. And on the other side, we have negative 11. Then we divide both sides of the equation by 22 X's negative 1/2. The next thing to do is to find the value of y. So let's go back to our equations and label them one and two, and I'm going to substitute the X value. I just got into one of the equations. How about equation one? So that would be 18 times negative. 1/2 minus 15. Why equals one? So that's negative. Nine. Minus 15 y equals one. Add nine to both sides and negative. 15 y equals 10. Then we'll divide both sides of that by negative 15 and that gives us why equals negative 2/3. Now it's a good idea to check this answer. So we have negative 2/3 for why and negative 1/2 for X, and we're going to check those into equation number two, so I'll make some space for that. So equation number two was 10 X minus 12 y equals three, substituting in their negative 1/2 for X and negative. 2/3 for why? And we'll see if we get three 10 times negative. 1/2 is negative. Five negative, 12 times negative. 2/3 is positive. Eight and negative. Five plus eight is three. That checks. That's good. Okay, so now we write our answer as an ordered pair X comma Y negative 1/2 comma. Negative. 2/3 hoops. Do that again. Negative 2/3. Okay.

Get More Help with this Textbook