We are given a system of two linear equations with two variables, $x$ and $y$: $7x - 6y = 30$ $2x + 6y = 24$ Our goal is to find the values of $x$ and $y$ that satisfy both equations.

1. Problem Description

We are given a system of two linear equations with two variables, $x$ and $y$:

$7x - 6y = 30$

$2x + 6y = 24$

Our goal is to find the values of $x$ and $y$ that satisfy both equations.

2. Solution Steps

We can solve this system of equations using the elimination method. Notice that the coefficients of $y$ in the two equations are $-6$ and $6$, so adding the two equations will eliminate $y$.

Adding the two equations gives:

$(7x - 6y) + (2x + 6y) = 30 + 24$

$7x + 2x - 6y + 6y = 54$

$9x = 54$

Now, we can solve for $x$ by dividing both sides by 9:

$x = \frac{54}{9}$

$x = 6$

Now that we have the value of $x$, we can substitute it into either equation to solve for $y$. Let's use the second equation:

$2x + 6y = 24$

$2(6) + 6y = 24$

$12 + 6y = 24$

Subtract 12 from both sides:

$6y = 24 - 12$

$6y = 12$

Divide both sides by 6:

$y = \frac{12}{6}$

$y = 2$

Therefore, the solution to the system of equations is $x = 6$ and $y = 2$.

3. Final Answer

$x = 6, y = 2$