Answer
The solution is $(3, 0)$.
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:
$2x + 3y = 6$
$2x - 3y = 6$
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$2x = 6$
$2x = 6$
Now we add both sides of the two equations to get:
$$4x = 12$$
Divide by $4$ to solve for $x$:
$$x = 3$$
Now that we have the value for $x$, we can plug this into one of the equations to solve for $y$. Let's use the first equation:
$$2(3) + 3y = 6$$
Multiply:
$$6 + 3y = 6$$
Subtract $6$ from both sides to isolate the variable on one side and constants on the other:
$$3y = 0$$
Divide both sides by $3$ to solve for $y$:
$$y = 0$$
The solution is $(3, 0)$.
