Answer
The solution is $(\frac{17}{7}, 1)$.
Work Step by Step
The coefficients of the $x$ term differ only in sign, so if we add these equations without modification, we will cancel out the $x$ term and can then solve for $y$:
Let us add the equations. First, we cancel out the $x$ term:
$7x - 4y = 13$
$-7x + 6y = -11$
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$-4y = 13$
$6y = -11$
Now we add both sides of the two equations to get:
$2y = 2$
Divide both sides of the equation by $2$ to solve for $y$:
$y = 1$
Now that we have the value for $y$, we can plug this value into one of the equations to solve for $x$. Let's use the first equation:
$7x - 4(1) = 13$
Multiply:
$7x - 4 = 13$
Add $4$ to each side of the equation to isolate the variable on one side of the equation and constants on the other:
$7x = 17$
Divide each side of the equation by $7$ to solve for $x$:
$x = \frac{17}{7}$
The solution is $(\frac{17}{7}, 1)$.