Use substitution to solve the system. 3y+ 16 = x %3D Зх- 5у %3D 28 y = %3D

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Solving a System of Linear Equations Using Substitution

**Linear Systems**

---

**Solving a system of linear equations using substitution**

Use [substitution](#) to solve the [system](#).

\[ 
\begin{cases}
3y + 16 = x \\
3x - 5y = 28
\end{cases}
\]

Below the equations, there are two empty fields for answers, labeled \( x = \) and \( y = \).

Next to the answer fields, there is a control panel with the following buttons:

- A checkbox icon
- An undo icon
- A question mark icon

The checkbox icon is likely used for submitting the answer. The undo icon is used to clear the input fields. The question mark icon is likely a help button, providing hints or additional resources to assist with solving the system of equations.

### Detailed Steps for Solving by Substitution:

1. **Solve one of the equations for one variable.**
   
   From the first equation:
   \[
   x = 3y + 16
   \]

2. **Substitute this expression into the other equation.**

   Substitute \( x \) in the second equation:
   \[
   3(3y + 16) - 5y = 28
   \]

3. **Solve the resulting single-variable equation.**
   
   Simplify and solve for \( y \):
   \[
   9y + 48 - 5y = 28 \\
   4y + 48 = 28 \\
   4y = 28 - 48 \\
   4y = -20 \\
   y = -5
   \]

4. **Substitute the value of \( y \) back into the equation from step 1 to find \( x \).**
   
   \[
   x = 3(-5) + 16 \\
   x = -15 + 16 \\
   x = 1
   \]

The solution to the system of equations is:

\[ 
x = 1 
\]

\[ 
y = -5 
\]

Enter these values into the respective fields and use the checkbox icon to submit your answer. If you make an error, you can use the undo icon to start over. For more help, click on the question mark icon.
Transcribed Image Text:### Solving a System of Linear Equations Using Substitution **Linear Systems** --- **Solving a system of linear equations using substitution** Use [substitution](#) to solve the [system](#). \[ \begin{cases} 3y + 16 = x \\ 3x - 5y = 28 \end{cases} \] Below the equations, there are two empty fields for answers, labeled \( x = \) and \( y = \). Next to the answer fields, there is a control panel with the following buttons: - A checkbox icon - An undo icon - A question mark icon The checkbox icon is likely used for submitting the answer. The undo icon is used to clear the input fields. The question mark icon is likely a help button, providing hints or additional resources to assist with solving the system of equations. ### Detailed Steps for Solving by Substitution: 1. **Solve one of the equations for one variable.** From the first equation: \[ x = 3y + 16 \] 2. **Substitute this expression into the other equation.** Substitute \( x \) in the second equation: \[ 3(3y + 16) - 5y = 28 \] 3. **Solve the resulting single-variable equation.** Simplify and solve for \( y \): \[ 9y + 48 - 5y = 28 \\ 4y + 48 = 28 \\ 4y = 28 - 48 \\ 4y = -20 \\ y = -5 \] 4. **Substitute the value of \( y \) back into the equation from step 1 to find \( x \).** \[ x = 3(-5) + 16 \\ x = -15 + 16 \\ x = 1 \] The solution to the system of equations is: \[ x = 1 \] \[ y = -5 \] Enter these values into the respective fields and use the checkbox icon to submit your answer. If you make an error, you can use the undo icon to start over. For more help, click on the question mark icon.
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