Chapter 5: Q. 151 (page 626)

Solve a System of Equations by Elimination -
$3 x + 8 y = 67 5 x + 3 y = 60$

Short Answer

Expert verified

The simplification of Expression will be - $(9, 5)$ .

Step by step solution

Step 1. Given Information.

Equation - $3 x + 8 y = 67 5 x + 3 y = 60$

Step 2. To Find

Solve a System of Equations by Elimination and find the value of x and y.

Step 3. Explanation

Equation -

$3 x + 8 y = 67 5 x + 3 y = 60$

We can eliminate y's by multiplying the first equation by 3 and second equation by 8 -

$(3 x + 8 y) \times 3 = 67 \times 3 (5 x + 3 y) \times 8 = 60 \times 8 9 x + 24 y = 201 40 x + 24 y = 480$

Step 4. Calculation

The equation become -

$9 x + 24 y = 201 40 x + 24 y = 480$

We subtract the x's and y's and constants -

$\begin{array}{l} 9 x + 24 y = 201 \\ \frac{40 x + 24 y = 480}{- 31 x = - 279} \end{array}$

Solve for x -

$x = 9$

Substitute $x = 9$ into the second equation $5 x + 3 y = 60$ , Then Solve for y -

$5 x + 3 y = 60 5 \times 9 + 3 y = 60 45 + 3 y = 60 3 y = 60 - 45 3 y = 15 y = 5$

Written as $(x, y)$ will be $(9, 5)$

Step 5. Check the answer

Check that the ordered pair is a solution to both original equations -

Put $(9, 5)$ in the equations -

$3 x + 8 y = 67 3 \times 9 + 8 \times 5 = 67 27 + 40 = 67 67 = 67 5 x + 3 y = 60 5 \times 9 + 3 \times 5 = 60 45 + 15 = 60 60 = 60$

The Solution is - $(9, 5)$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve a System of Equations by Elimination -
$3 x + 8 y = 67 5 x + 3 y = 60$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. To Find

Step 3. Explanation

Step 4. Calculation

Step 5. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Logic and Functions

Calculus

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve a System of Equations by Elimination - 3x+8y=675x+3y=60

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. To Find

Step 3. Explanation

Step 4. Calculation

Step 5. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Logic and Functions

Calculus

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve a System of Equations by Elimination -
$3 x + 8 y = 67 5 x + 3 y = 60$