Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 5: Q. 5.56 (page 619)

Solve the system by elimination $\{\begin{cases} 7 x + 8 y = 4 \\ 3 x - 5 y = 27 \end{cases}$ .

Short Answer

Expert verified

The solution of the given system is $(x, y) = (4, - 3) .$

Step by step solution

Step 1. Given information

The given system is $\{\begin{cases} 7 x + 8 y = 4 \\ 3 x - 5 y = 27 \end{cases}$

Step 2. Solve for x

$\{\begin{cases} 7 x + 8 y = 4 \\ 3 x - 5 y = 27 \end{cases} given \{\begin{cases} 5 (7 x + 8 y = 4) Mutiplyonbothsideswith5 \\ 8 (3 x - 5 y = 27) Mutiplyonbothsideswith 8 \end{cases} \{\begin{cases} 35 x + 40 y = 20 \\ 24 x - 40 y = 216 \end{cases} Simplify \begin{array}{l} 35 x + 40 y = 20 \\ 24 x - 40 y = 216 \end{array} Addbothequations 59 x = 236 x = \frac{236}{59} solveforx x = 4$

Step 3. Solve for y

$\begin{array}{l} 7 x + 8 y = 4 Firstequation \\ \begin{array}{l} 7 (4) + 8 y = 4 Substitute x = 4 \\ 28 + 8 y = 4 Solvefor y \\ 8 y = 4 - 28 \\ 8 y = - 24 \\ y = - \frac{24}{8} \\ y = - 3 \end{array} \end{array}$

Hence, the solution is $(x, y) = (4, - 3) .$

Step 4. Verify the solution

$\begin{array}{l} 7 x + 8 y = 4 鈬� 7 (4) + 8 (- 3) = 4 \\ 28 - 24 = 4 \\ 4 = 4 true \\ 3 x - 5 y = 27 鈬� 3 (4) - 5 (- 3) = 27 \\ 12 + 15 = 27 \\ 27 = 27 true \end{array}$

Both equations are true.

Hence, the solution is $(x, y) = (4, - 3) .$

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91影视

Solve the system by elimination $\{\begin{cases} 7 x + 8 y = 4 \\ 3 x - 5 y = 27 \end{cases}$ .

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 elimination7x+8y=43x-5y=27.

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

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Solve the system by elimination $\{\begin{cases} 7 x + 8 y = 4 \\ 3 x - 5 y = 27 \end{cases}$ .