This problem involves solving a system of equations by substitution or elimination. The system given is:

$x = 5y + 4$ $x = 3y + 18$

Since both expressions are equal to $x$, we can set them equal to each other:

$5y + 4 = 3y + 18$

Step-by-Step Solution

1. Isolate terms with $y$: Subtract $3y$ from both sides: $5y - 3y + 4 = 18$ Simplifying this, we get: $2y + 4 = 18$

2. Solve for $y$: Subtract 4 from both sides: $2y = 14$ Now, divide by 2: $y = 7$

3. Substitute $y = 7$ back into one of the original equations to find $x$. Using $x = 5y + 4$: $x = 5(7) + 4$ $x = 35 + 4$ $x = 39$

Solution

The solution to the system is: $x = 39, \quad y = 7$

Would you like more details or have any questions?

Related Questions

1. How would the solution change if the equations had different coefficients?
2. Can this system be solved using the elimination method, and if so, how?
3. What would the result be if $y$ had a different value in one equation?
4. How can you verify if your solution to a system of equations is correct?
5. What happens when two lines in a system of linear equations are parallel?

Tip

For systems of equations, setting the two expressions for $x$ (or $y$) equal to each other can simplify the process, especially if both are already solved for the same variable.