Chapter 13: Chapter 13

Problem 296

Solve the equations $3 \mathrm{x}+2 \mathrm{y}=1$ and $5 \mathrm{x}-3 \mathrm{y}=8$ simultaneously.

Short Answer

Expert verified

The solution to the given system of equations $3x + 2y = 1$ and $5x - 3y = 8$ is the ordered pair $(x, y) = (1, -1)$.

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Step by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Write the system of equations

First, let's write down the given system of equations. $3x + 2y = 1$ (1) $5x - 3y = 8$ (2)

Step 2: Multiply each equation to make coefficients of y the same in absolute value

In order to eliminate one of the variables using the elimination method, we need the coefficients of y to be the same in both equations so that they cancel each other out when adding or subtracting the equations. To do so, we will multiply equation (1) by 3 and equation (2) by 2. Equation (1) * 3: $9x + 6y = 3$ (3) Equation (2) * 2: $10x - 6y = 16$ (4)

Step 3: Add the new equations to eliminate y

Now that both new equations have the same coefficient for y, we can add them together to eliminate y. (3) + (4): $9x + 6y + 10x - 6y = 3 + 16$ $19x = 19$

Step 4: Solve for x

Now we have a simple linear equation with only one variable. Solve for x: $19x = 19 \Rightarrow x = \frac{19}{19} = 1$

Step 5: Substitute the value of x back into one of the original equations to find y

Now that we have the value for x, we can substitute it back into one of the original equations to find the value of y. Let's use equation (1) for this: $3x + 2y = 1 \Rightarrow 3(1) + 2y = 1$

Step 6: Solve for y

Now we have a linear equation with only one variable, y. Solve for y: $3 + 2y = 1 \Rightarrow 2y = -2 \Rightarrow y = \frac{-2}{2} = -1$

Step 7: Write the solution as an ordered pair

Now that we have the values of x and y, we can write the solution as an ordered pair: $(x, y) = (1, -1)$ So, the solution to the system of equations is (1, -1).

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Chapter 13: Chapter 13

Solve the equations \(3 \mathrm{x}+2 \mathrm{y}=1\) and $5 \mathrm{x}-3 \mathrm{y}=8$ simultaneously.

Short Answer

Step by step solution

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Step 1: Write the system of equations

Step 2: Multiply each equation to make coefficients of y the same in absolute value

Step 3: Add the new equations to eliminate y

Step 4: Solve for x

Step 5: Substitute the value of x back into one of the original equations to find y

Step 6: Solve for y

Step 7: Write the solution as an ordered pair

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Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 14

Chapter 15

Chapter 16

Chapter 17

Chapter 18

Chapter 19

Chapter 20

Chapter 21

Chapter 22

Chapter 23

Chapter 24

Chapter 25

Chapter 26

Chapter 27

Chapter 28

Chapter 29

Chapter 30

Chapter 31

Chapter 32

Chapter 33

Chapter 34

Chapter 35

Chapter 36

Chapter 37

Chapter 38

Chapter 39

Chapter 40

Chapter 41

Chapter 42

Chapter 43

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