College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.1: Systems Of Linear Equations
Problem 83E: Use the system of three equations in three variables to solve each problem. Work schedules A college...
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![### Solving a System of Linear Equations
**Solve the following system of equations:**
\[
\begin{cases}
2x - 3y = 4 \\
-2x + 6y = -10
\end{cases}
\]
In order to find the values of \( x \) and \( y \) that simultaneously satisfy both equations, use one of the methods for solving systems of linear equations, such as substitution, elimination, or matrix methods.
#### Graphical Representation
There is a pad on the left showing placeholders for \( x \) and \( y \):
\[
\begin{cases}
x = \_\_ \\
y = \_\_
\end{cases}
\]
On the right, there are a few interactive icons, typically found in educational software. The icons shown are:
- A checker icon: It might be for submitting or verifying the solution.
- An "Undo" arrow: Possibly for resetting the input or correcting mistakes.
- A trash bin icon: It could be to clear the existing inputs.
- A "Question Mark": Likely for further help or hints.
To solve, follow these steps:
1. **Elimination Method**:
- Add the two equations:
\[
2x - 3y + (-2x + 6y) = 4 + (-10)
\]
\[
0x + 3y = -6
\]
\[
3y = -6 \implies y = -2
\]
- Substitute \( y = -2 \) back into one of the original equations:
\[
2x - 3(-2) = 4
\]
\[
2x + 6 = 4
\]
\[
2x = -2
\]
\[
x = -1
\]
2. Verify by substituting \( x = -1 \) and \( y = -2 \) back into the second equation:
\[
-2(-1) + 6(-2) = -10
\]
\[
2 - 12 = -10 \implies -10 = -10 \text{ (True) }
\]
**Solution:**
\[
\begin{cases}
x =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9a4d797-fb4e-4740-aaae-e63d5fa53795%2F5517159f-77a7-4338-9b31-c1ff612ccf39%2Fpge6xv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving a System of Linear Equations
**Solve the following system of equations:**
\[
\begin{cases}
2x - 3y = 4 \\
-2x + 6y = -10
\end{cases}
\]
In order to find the values of \( x \) and \( y \) that simultaneously satisfy both equations, use one of the methods for solving systems of linear equations, such as substitution, elimination, or matrix methods.
#### Graphical Representation
There is a pad on the left showing placeholders for \( x \) and \( y \):
\[
\begin{cases}
x = \_\_ \\
y = \_\_
\end{cases}
\]
On the right, there are a few interactive icons, typically found in educational software. The icons shown are:
- A checker icon: It might be for submitting or verifying the solution.
- An "Undo" arrow: Possibly for resetting the input or correcting mistakes.
- A trash bin icon: It could be to clear the existing inputs.
- A "Question Mark": Likely for further help or hints.
To solve, follow these steps:
1. **Elimination Method**:
- Add the two equations:
\[
2x - 3y + (-2x + 6y) = 4 + (-10)
\]
\[
0x + 3y = -6
\]
\[
3y = -6 \implies y = -2
\]
- Substitute \( y = -2 \) back into one of the original equations:
\[
2x - 3(-2) = 4
\]
\[
2x + 6 = 4
\]
\[
2x = -2
\]
\[
x = -1
\]
2. Verify by substituting \( x = -1 \) and \( y = -2 \) back into the second equation:
\[
-2(-1) + 6(-2) = -10
\]
\[
2 - 12 = -10 \implies -10 = -10 \text{ (True) }
\]
**Solution:**
\[
\begin{cases}
x =
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