To solve the system of linear equations:
[tex]\[
\begin{array}{l}
y - 4x = 7 \\
2y + 4x = 2
\end{array}
\][/tex]
we can use the following steps:
### Step 1: Write the equations in a standard form:
We already have the system of equations in standard form:
1. [tex]\( y - 4x = 7 \)[/tex]
2. [tex]\( 2y + 4x = 2 \)[/tex]
### Step 2: Add the two equations:
First, we add the first and second equations to eliminate [tex]\(x\)[/tex]:
[tex]\[ y - 4x + 2y + 4x = 7 + 2 \][/tex]
Simplifying, we get:
[tex]\[ 3y = 9 \][/tex]
### Step 3: Solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{9}{3} = 3 \][/tex]
So, [tex]\( y = 3 \)[/tex].
### Step 4: Substitute [tex]\( y \)[/tex] back into one of the original equations to solve for [tex]\( x \)[/tex]:
Using the first equation:
[tex]\[ 3 - 4x = 7 \][/tex]
[tex]\[ 3 - 7 = 4x \][/tex]
[tex]\[ -4 = 4x \][/tex]
[tex]\[ x = -1 \][/tex]
### Solution
The solution to the system of equations is [tex]\( x = -1 \)[/tex] and [tex]\( y = 3 \)[/tex].
Thus, the answer to the given system of equations is:
[tex]\[ (-1, 3) \][/tex]
So, the correct option is:
[tex]\[
\boxed{(-1, 3)}
\][/tex]
