Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 5: Q. 5.58 (page 621)

Solve the system by elimination $\{\begin{cases} x + \frac{3}{5} y = - \frac{1}{5} \\ - \frac{1}{2} x - \frac{2}{3} y = \frac{5}{6} \end{cases}$ .

Short Answer

Expert verified

The solution of the system is $(x, y) = (1, - 2) .$

Step by step solution

Step 1. Given information

The given system is $\{\begin{cases} x + \frac{3}{5} y = - \frac{1}{5} \\ - \frac{1}{2} x - \frac{2}{3} y = \frac{5}{6} \end{cases}$

Step 2. Remove fractions

$\{\begin{cases} x + \frac{3}{5} y = - \frac{1}{5} \\ - \frac{1}{2} x - \frac{2}{3} y = \frac{5}{6} \end{cases} Given \{\begin{cases} 5 (x + \frac{3}{5} y) = 5 (- \frac{1}{5}) Multiplyonbothsideswith5 \\ 6 (- \frac{1}{2} x - \frac{2}{3} y) = 6 (\frac{5}{6}) Multiplyonbothsideswith6 \end{cases} \{\begin{cases} 5 x + 3 y = - 1 \\ - 3 x - 4 y = 5 \end{cases} Simplify$

Step 3. Solve for y

$\{\begin{cases} 5 x + 3 y = - 1 \\ - 3 x - 4 y = 5 \end{cases} \{\begin{cases} 3 (5 x + 3 y) = 3 (- 1) Multiplyonbothsideswith3 \\ 5 (- 3 x - 4 y) = 5 (5) Multiplyonbothsideswith5 \end{cases} \{\begin{cases} 15 x + 9 y = - 3 \\ - 15 x - 20 y = 25 \end{cases} Simplify$

Add both equations

$\begin{array}{l} 15 x + 9 y = - 3 \\ - 15 x - 20 y = 25 \end{array} - 11 y = 22 y = \frac{22}{- 11} Solvefor y y = - 2$

Step 4. Solve for x

$x + \frac{3}{5} y = - \frac{1}{5} firstequation x + \frac{3}{5} (- 2) = - \frac{1}{5} Substitute y = - 2 x + \frac{- 6}{5} = - \frac{1}{5} Solvefor x x = - \frac{1}{5} + \frac{6}{5} x = \frac{- 1 + 6}{5} x = 1$

Hence, the solution is $(x, y) = (1, - 2) .$

Step 5. Verify the solution

$x + \frac{3}{5} y = - \frac{1}{5} 鈬� 1 + \frac{3}{5} (- 2) = - \frac{1}{5} 1 + \frac{- 6}{5} = - \frac{1}{5} \frac{5 - 6}{5} = - \frac{1}{5} - \frac{1}{5} = - \frac{1}{5} true - \frac{1}{2} x - \frac{2}{3} y = \frac{5}{6} 鈬� - \frac{1}{2} (1) - \frac{2}{3} (- 2) = \frac{5}{6} - \frac{1}{2} + \frac{4}{3} = \frac{5}{6} \frac{- 3 + 8}{6} = \frac{5}{6} \frac{5}{6} = \frac{5}{6} true$

Both equations are true.

Hence, the solution is $(x, y) = (1, - 2) .$

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91影视

Solve the system by elimination $\{\begin{cases} x + \frac{3}{5} y = - \frac{1}{5} \\ - \frac{1}{2} x - \frac{2}{3} y = \frac{5}{6} \end{cases}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Remove fractions

Step 3. Solve for y

Step 4. Solve for x

Step 5. Verify the solution

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91影视

Solve the system by eliminationx+35y=-15-12x-23y=56.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Remove fractions

Step 3. Solve for y

Step 4. Solve for x

Step 5. Verify the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Calculus

Mechanics Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

Solve the system by elimination $\{\begin{cases} x + \frac{3}{5} y = - \frac{1}{5} \\ - \frac{1}{2} x - \frac{2}{3} y = \frac{5}{6} \end{cases}$ .