Chapter 4: Q. 410 (page 485)

In the following exercises, solve each system of equations. Use either substitution or elimination.
$\{\begin{cases} - 3 x + 4 y = 25 \\ x - 5 y = - 23 \end{cases}$

Short Answer

Expert verified

The solution to the system of equations $\{\begin{cases} - 3 x + 4 y = 25 \\ x - 5 y = - 23 \end{cases}$ is $(- 3, 4)$

Step by step solution

Step 1. Given

The system of equations $\{\begin{cases} - 3 x + 4 y = 25 \\ x - 5 y = - 23 \end{cases}$

To find the solution of the system of equations.

Step 2. Solve the equations

Consider the system of equations:

$- 3 x + 4 y = 25$

$x - 5 y = - 23$

Solve the second equation for $x$ ,

$x = - 23 + 5 y$

Step 3. Solve for y

Substitute $x = - 23 + 5 y$ in the first equation,

$- 3 x + 4 y = 25$

$- 3 (- 23 + 5 y) + 4 y = 25$

$69 - 15 y + 4 y = 25$

$- 11 y = 25 - 69$

$- 11 y = - 44$

Divide both sides of the equation by $- 11$ ,

$y = 4$

Step 4. Solve for x

Substitute $y = 4$ in the second equation,

$x - 5 y = - 23$

$x - 5 (4) = - 23$

$x = - 23 + 20$

$x = - 3$

The solution of the system of equation is $(- 3, 4)$

Step 5. Check the solution

Substitute $(- 3, 4)$ in both the equations,

$- 3 x + 4 y = 25$

$- 3 (- 3) + 4 (4) = 25$

$9 + 16 = 25$

$25 = 25$ is true.

Then, $x - 5 y = - 23$

$(- 3) - 5 (4) = - 23$

$- 23 = - 23$ is true.

Hence the solution has been checked.

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.

In the following exercises, solve each system of equations. Use either substitution or elimination.
$\{\begin{cases} - 3 x + 4 y = 25 \\ x - 5 y = - 23 \end{cases}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Solve the equations

Step 3. Solve for y

Step 4. Solve for x

Step 5. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Decision Maths

Statistics

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each system of equations. Use either substitution or elimination.-3x+4y=25x-5y=-23

Short Answer

Step by step solution

Step 1. Given

Step 2. Solve the equations

Step 3. Solve for y

Step 4. Solve for x

Step 5. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Decision Maths

Statistics

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each system of equations. Use either substitution or elimination.
$\{\begin{cases} - 3 x + 4 y = 25 \\ x - 5 y = - 23 \end{cases}$