What is the value of x in the solution to the system of linear equations?
{y=3x+2 y=x-4     -7     -3     1   5

Let's solve the given system of linear equations:

\[
\begin{aligned}
y &= 3x + 2 \quad \text{(Equation 1)} \\
y &= x - 4 \quad \text{(Equation 2)}
\end{aligned}
\]

### Step 1: Set the two equations equal to each other
Since both equations equal \( y \), we can set them equal to each other:

\[
3x + 2 = x - 4
\]

### Step 2: Solve for \( x \)
Now, solve the equation:

\[
3x + 2 = x - 4
\]

Subtract \( x \) from both sides:

\[
3x - x + 2 = -4
\]

This simplifies to:

\[
2x + 2 = -4
\]

Now, subtract 2 from both sides:

\[
2x = -6
\]

Finally, divide both sides by 2:

\[
x = -3
\]

### Step 3: Find \( y \)
Now that we know \( x = -3 \), we can substitute this value into either of the original equations to find \( y \). Let’s use Equation 2:

\[
y = x - 4
\]

Substitute \( x = -3 \):

\[
y = -3 - 4 = -7
\]

### Final Answer:
The solution to the system of equations is:

\[
x = -3 \quad \text{and} \quad y = -7
\]

Would you like any more details on solving systems of equations? Or do you have other questions?

### Related Questions:
1. How can you solve a system of linear equations using substitution?
2. What is the graphical method of solving a system of equations?
3. How do you handle a system of equations with no solution or infinite solutions?
4. What is the method of solving systems of equations by elimination?
5. How do you solve a system of three equations with three unknowns?

**Tip**: Always check the solution by substituting the values of \( x \) and \( y \) into both original equations to ensure they satisfy both.

What is the value of x in the solution to the system of linear equations? {y=3x+2 y=x-4}

Learn how to solve the system of linear equations y=3x+2 and y=x-4 with a detailed step-by-step solution. This problem uses the substitution method to find the values of x and y. Suitable for students in Grades 7-9.

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