https://file.aiquickdraw.com/mathbot/file/1728650761424pnza6291.jpg

The system of equations given in the image is:

1. \( 3x - 14 = 0 \)
2. \( x - 4y + 1 = 0 \)

### Step 1: Solve the first equation for \( x \)
From the first equation:
\[
3x - 14 = 0
\]
Add 14 to both sides:
\[
3x = 14
\]
Now, divide both sides by 3:
\[
x = \frac{14}{3}
\]

### Step 2: Substitute \( x = \frac{14}{3} \) into the second equation
Substitute the value of \( x \) into the second equation \( x - 4y + 1 = 0 \):
\[
\frac{14}{3} - 4y + 1 = 0
\]
Simplify the constants:
\[
\frac{14}{3} + 1 = \frac{14}{3} + \frac{3}{3} = \frac{17}{3}
\]
So the equation becomes:
\[
\frac{17}{3} - 4y = 0
\]
Now, subtract \( \frac{17}{3} \) from both sides:
\[
-4y = -\frac{17}{3}
\]
Divide both sides by -4:
\[
y = \frac{17}{12}
\]

### Solution:
The solution to the system of equations is:
\[
x = \frac{14}{3}, \quad y = \frac{17}{12}
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you solve a system of linear equations using substitution?
2. What is the process for solving equations involving fractions?
3. How do you check if the solution to a system of equations is correct?
4. Can we solve the same system of equations using the elimination method?
5. How do you solve for variables in a system where both equations contain fractions?

### Tip:
When solving systems of equations, it's often easier to simplify one equation fully before substituting into the other to avoid unnecessary complexity.

Solve the system of equations: 3x - 14 = 0 and x - 4y + 1 = 0

Learn how to solve the system of linear equations 3x - 14 = 0 and x - 4y + 1 = 0 using the substitution method. This problem covers key algebraic concepts and is suitable for students in Grades 8-10.

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