https://file.aiquickdraw.com/mathbot/file/17303984836933tb9n6kp.jpg

To solve this system of equations using substitution, let’s follow these steps:

Given equations:
1. \( y = 3x + 1 \)
2. \( 2y - x = 12 \)

### Step 1: Substitute \( y \) from the first equation into the second equation.
Since \( y = 3x + 1 \), we can replace \( y \) in the second equation:
\[
2(3x + 1) - x = 12
\]

### Step 2: Expand and simplify the equation.
\[
6x + 2 - x = 12
\]
Combine like terms:
\[
5x + 2 = 12
\]

### Step 3: Solve for \( x \).
Subtract 2 from both sides:
\[
5x = 10
\]
Now, divide by 5:
\[
x = 2
\]

### Step 4: Substitute \( x = 2 \) back into the first equation to find \( y \).
\[
y = 3(2) + 1
\]
\[
y = 6 + 1
\]
\[
y = 7
\]

### Solution
The solution to the system is:
\[
(x, y) = (2, 7)
\]

Would you like more details or have any questions?

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Here are 5 related questions to expand on this topic:
1. What would be the steps if we used elimination instead of substitution to solve this system?
2. How can we verify if a given solution is correct for a system of equations?
3. What are some common types of solutions (unique, infinite, or no solution) in systems of linear equations?
4. How does substitution work when both equations are solved for \( y \) or \( x \) instead of just one?
5. What is the graphical interpretation of the solution to this system of equations?

**Tip:** Always check your solution by plugging the values back into both original equations to ensure they hold true.

Solve this system of equations by using substitution:
 y = 3x + 1
 2y - x = 12

Learn how to solve the system of equations y = 3x + 1 and 2y - x = 12 using substitution. This step-by-step solution covers key algebraic techniques and concepts suitable for students in Grades 8-10.

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