Answer
The solution is $(4, 1)$.
Work Step by Step
The coefficients of the $y$ term differ only in sign, so if we add these equations without modification, we will cancel out the $y$ term and can then solve for $x$:
Let us add the equations. First, we cancel out the $y$ term:
$3x + 2y = 14$
$3x - 2y = 10$
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$3x = 14$
$3x = 10$
Now we add both sides of the two equations to get:
$6x = 24$
Divide each side by $6$ to solve for $x$:
$x = 4$
Now that we have the value for $x$, we can plug this value into one of the equations to solve for $y$. Let's use the first equation:
$3(4) + 2y = 14$
Multiply:
$12 + 2y = 14$
Subtract $12$ from each side of the equation to isolate the variable on one side and constants on the other:
$2y = 2$
Divide both sides by $2$ to solve for $y$:
$y = 1$
The solution is $(4, 1)$.
