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.