Chapter 4: Q 38. (page 386)

Solve the system of equations by substitution
$\{\begin{cases} 2 x + y = 5 \\ x - 2 y = - 15 \end{cases}$

Short Answer

Expert verified

The solution for the system of equations is,

$x = - 1 y = 7$ .

Step by step solution

Step 1. Given the information

The system of equations is,

$\{\begin{cases} 2 x + y = 5 \\ x - 2 y = - 15 \end{cases}$

Step 2. Solve the first equation for y

Solving the equation $2 x + y = 5$ for $y$

$2 x + y = 5$

$y = 5 - 2 x$

Step 3. Substituting the value of y in the equation.

Substituting $y = 5 - 2 x$ in the equation

$x - 2 y = - 15$

$x - 2 (5 - 2 x) = - 15$

$x - 10 + 4 x = - 15$

$5 x - 10 = - 15$

$5 x = - 15 + 10$

$5 x = - 5$

$x = - 5 \div 5$

$x = - 1$

Step 4. Substituting the value of x in the equation

Substituting $x = - 1$ in the equation

$y = 5 - 2 x$

$y = 5 - 2 (- 1)$

$y = 5 + 2$

$y = 7$

Step 5. Checking the solution for the equation 2x+y=5.

Substituting $x = - 1 y = 7$ in the equation

$2 x + y = 5$

$2 (- 1) + 7 = 5$

$- 2 + 7 = 5$

$5 = 5$

This is true.

Step 6. Checking the solution for the equation x-2y=-15

Substituting $x = - 1 y = 7$ in the equation

$x - 2 y = - 15$

$- 1 - 2 (7) = - 15$

$- 1 - 14 = - 15$

$- 15 = - 15$

This is true.

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 the system of equations by substitution
$\{\begin{cases} 2 x + y = 5 \\ x - 2 y = - 15 \end{cases}$

Short Answer

Step by step solution

Step 1. Given the information

Step 2. Solve the first equation for y

Step 3. Substituting the value of y in the equation.

Step 4. Substituting the value of x in the equation

Step 5. Checking the solution for the equation 2x+y=5.

Step 6. Checking the solution for the equation x-2y=-15

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Geometry

Logic and Functions

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve the system of equations by substitution2x+y=5x-2y=-15

Short Answer

Step by step solution

Step 1. Given the information

Step 2. Solve the first equation for y

Step 3. Substituting the value of y in the equation.

Step 4. Substituting the value of x in the equation

Step 5. Checking the solution for the equation 2x+y=5.

Step 6. Checking the solution for the equation x-2y=-15

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Geometry

Logic and Functions

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve the system of equations by substitution
$\{\begin{cases} 2 x + y = 5 \\ x - 2 y = - 15 \end{cases}$