Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 5: Q. 5.57 (page 621)

Solve the system by elimination $\{\begin{cases} \frac{1}{3} x - \frac{1}{2} y = 1 \\ \frac{3}{4} x - y = \frac{5}{2} \end{cases}$ .

Short Answer

Expert verified

The solution of the given system is $(x, y) = (6, 2) .$

Step by step solution

Step 1. Given information

The given system is $\{\begin{cases} \frac{1}{3} x - \frac{1}{2} y = 1 \\ \frac{3}{4} x - y = \frac{5}{2} \end{cases}$

Step 2. Remove the fractions

$\{\begin{cases} \frac{1}{3} x - \frac{1}{2} y = 1 \\ \frac{3}{4} x - y = \frac{5}{2} \end{cases} given \{\begin{cases} 6 (\frac{1}{3} x - \frac{1}{2} y) = 6 (1) Multiplyonbothsideswith6 \\ 4 (\frac{3}{4} x - y) = 4 (\frac{5}{2}) Multiplyonbothsideswith4 \end{cases} \{\begin{cases} 2 x - 3 y = 6 \\ 3 x - 4 y = 10 \end{cases}$

Step 3. Solve for y

$\{\begin{cases} 2 x - 3 y = 6 \\ 3 x - 4 y = 10 \end{cases} \{\begin{cases} - 3 (2 x - 3 y) = - 3 (6) Multiplyonbothsideswith-3 \\ 2 (3 x - 4 y) = 2 (10) Multiplyonbothsideswith2 \end{cases} \{\begin{cases} - 6 x + 9 y = - 18 \\ 6 x - 8 y = 20 \end{cases} Simplify$

Add both equations

$\begin{array}{l} - 6 x + 9 y = - 18 \\ 6 x - 8 y = 20 \end{array} y = 2$

Step 4. Solve for x

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

Hence, the solution is $(x, y) = (6, 2) .$

Step 5. Verify the solution

$\begin{array}{l} \frac{1}{3} x - \frac{1}{2} y = 1 鈬� \frac{1}{3} (6) - \frac{1}{2} (2) = 1 \\ 2 - 1 = 1 \\ 1 = 1 true \\ \frac{3}{4} x - y = \frac{5}{2} 鈬� \frac{3}{4} (6) - (2) = \frac{5}{2} \\ \frac{18 - 8}{4} = \frac{5}{2} \\ \frac{10}{4} = \frac{5}{2} \\ \frac{5}{2} = \frac{5}{2} true \end{array}$

Both equations are true.

Hence, the solution is $(x, y) = (6, 2) .$

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91影视

Solve the system by elimination $\{\begin{cases} \frac{1}{3} x - \frac{1}{2} y = 1 \\ \frac{3}{4} x - y = \frac{5}{2} \end{cases}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Remove the 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 elimination13x-12y=134x-y=52.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Remove the 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

Calculus

Discrete Mathematics

Mechanics Maths

Decision Maths

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Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve the system by elimination $\{\begin{cases} \frac{1}{3} x - \frac{1}{2} y = 1 \\ \frac{3}{4} x - y = \frac{5}{2} \end{cases}$ .