Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![**Solve the system of equations:**
\[
\begin{cases}
32x - 8y = 38 \\
-40x - 8y = -70
\end{cases}
\]
---
To solve the system of equations, consider using either the substitution method or the elimination method. Here, both equations can be manipulated in a way that allows for the elimination of one of the variables.
1. **Equation (1):** \( 32x - 8y = 38 \)
2. **Equation (2):** \( -40x - 8y = -70 \)
Notice that both equations have the term \(-8y\), which can be easily eliminated by subtracting one equation from the other. Follow these steps to solve the system by elimination:
- Subtract Equation (2) from Equation (1):
\[
(32x - 8y) - (-40x - 8y) = 38 - (-70)
\]
Simplify the above:
\[
32x + 40x = 38 + 70
\]
\[
72x = 108
\]
\[
x = \frac{108}{72} = 1.5
\]
Now, substitute \(x = 1.5\) back into either original equation to solve for \(y\). Using Equation (1):
\[
32(1.5) - 8y = 38
\]
\[
48 - 8y = 38
\]
\[
-8y = 38 - 48
\]
\[
-8y = -10
\]
\[
y = \frac{-10}{-8} = 1.25
\]
Therefore, the solution to the system of equations is \(x = 1.5\) and \(y = 1.25\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb740a2b9-45d2-4a76-b926-8ccc48491ca4%2F205d99aa-1409-4f64-becc-7b050eb91e22%2F9g35164_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve the system of equations:**
\[
\begin{cases}
32x - 8y = 38 \\
-40x - 8y = -70
\end{cases}
\]
---
To solve the system of equations, consider using either the substitution method or the elimination method. Here, both equations can be manipulated in a way that allows for the elimination of one of the variables.
1. **Equation (1):** \( 32x - 8y = 38 \)
2. **Equation (2):** \( -40x - 8y = -70 \)
Notice that both equations have the term \(-8y\), which can be easily eliminated by subtracting one equation from the other. Follow these steps to solve the system by elimination:
- Subtract Equation (2) from Equation (1):
\[
(32x - 8y) - (-40x - 8y) = 38 - (-70)
\]
Simplify the above:
\[
32x + 40x = 38 + 70
\]
\[
72x = 108
\]
\[
x = \frac{108}{72} = 1.5
\]
Now, substitute \(x = 1.5\) back into either original equation to solve for \(y\). Using Equation (1):
\[
32(1.5) - 8y = 38
\]
\[
48 - 8y = 38
\]
\[
-8y = 38 - 48
\]
\[
-8y = -10
\]
\[
y = \frac{-10}{-8} = 1.25
\]
Therefore, the solution to the system of equations is \(x = 1.5\) and \(y = 1.25\).
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