Q. 410 In the following exercises, solv... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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.

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91影视

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.

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91影视

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

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Probability and Statistics

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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