We are asked to solve the following system of linear equations without graphing: $7x + 11y = -2$ $7x + 3y = 30$

1. Problem Description

We are asked to solve the following system of linear equations without graphing:

$7x + 11y = -2$

$7x + 3y = 30$

2. Solution Steps

We will use the method of substitution or elimination. Since the coefficient of $x$ is the same in both equations, we can use elimination.

Subtract the second equation from the first:

$(7x + 11y) - (7x + 3y) = -2 - 30$

$7x + 11y - 7x - 3y = -32$

$8y = -32$

$y = \frac{-32}{8}$

$y = -4$

Now, substitute $y = -4$ into either equation. We'll use the first equation:

$7x + 11(-4) = -2$

$7x - 44 = -2$

$7x = -2 + 44$

$7x = 42$

$x = \frac{42}{7}$

$x = 6$

Therefore, the solution is $x = 6$ and $y = -4$.

We can check our solution in the second equation:

$7x + 3y = 30$

$7(6) + 3(-4) = 30$

$42 - 12 = 30$

$30 = 30$

The solution is correct.

3. Final Answer

$x = 6$, $y = -4$