Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 5: Q. 5.55 (page 619)

Solve the system by elimination $\{\begin{cases} 3 x - 4 y = - 9 \\ 5 x + 3 y = 14 \end{cases}$

Short Answer

Expert verified

The solution of the given system is $(x, y) = (1, 3) .$

Step by step solution

Step 1. Given information

The given system is $\{\begin{cases} 3 x - 4 y = - 9 \\ 5 x + 3 y = 14 \end{cases}$

Step 2. Solve for x

$\{\begin{cases} 3 x - 4 y = - 9 \\ 5 x + 3 y = 14 \end{cases} Given \{\begin{cases} 3 (3 x - 4 y) = 3 (- 9) Mutiplyonbothsideswith3 \\ 4 (5 x + 3 y) = 4 (14) Mutiplyonbothsideswith4 \end{cases} \{\begin{cases} 9 x - 12 y = - 27 \\ 20 x + 12 y = 56 \end{cases} Simplify$

Add both equations

$\begin{array}{l} 9 x - 12 y = - 27 \\ 20 x + 12 y = 56 \end{array} 29 x = 29 x = \frac{29}{29} Solvefor x x = 1$

Step 3. Solve for y

$\begin{array}{l} 9 x - 12 y = - 27 Firstequation \\ \begin{array}{l} 9 (1) - 12 y = - 27 substitute x = 1 \\ 9 - 12 y = - 27 Solvefor y \\ - 12 y = - 27 - 9 \\ - 12 y = - 36 \\ y = \frac{- 36}{- 12} \\ y = 3 \end{array} \end{array}$

Hence, the solution is $(x, y) = (1, 3) .$

Step 4. Verify the solution

$\begin{array}{l} 3 x - 4 y = - 9 鈬� 3 (1) - 4 (3) = - 9 \\ 3 - 12 = - 9 \\ - 9 = - 9 true \\ 5 x + 3 y = 14 鈬� 5 (1) + 3 (3) = 14 \\ 5 + 9 = 14 \\ 14 = 14 true \end{array}$

Both equations are true.

Hence, the solution is $(x, y) = (1, 3) .$

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91影视

Solve the system by elimination $\{\begin{cases} 3 x - 4 y = - 9 \\ 5 x + 3 y = 14 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve for x

Step 3. Solve for y

Step 4. Verify the solution

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91影视

Solve the system by elimination3x-4y=-95x+3y=14

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve for x

Step 3. Solve for y

Step 4. Verify the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve the system by elimination $\{\begin{cases} 3 x - 4 y = - 9 \\ 5 x + 3 y = 14 \end{cases}$