Answer
The solution is $\left(\dfrac{23}{14}, -\dfrac{13}{14}\right)$.
Work Step by Step
It looks like using the elimination method is an easier way to solve this equation.
First, we need to convert the equations so that one variable has opposite numerical coefficients. If we add these two equations together, we can eliminate that variable and just deal with one variable instead of two:
It is easier to get rid of the $y$ terms in both equations because we would only have to convert one equation instead of two. We multiply the first equation by $4$ to obtain the equivalent system:
$12x + 4y = 16$
$ 2x - 4y = 7$
Add the two equations together to come up with a single equation:
$(12x+4y)+(2x-4y)=16+7\\
14x = 23$
Divide both sides of the equation by $14$ to solve for $x$:
$x = \dfrac{23}{14}$
Now that we have the value for $x$, we can plug it into one of the equations to solve for $y$.
Let us plug in the value for $x$ into the first equation:
$3x+y=4\\
3\left(\dfrac{23}{14}\right) + y = 4\\
\dfrac{69}{14} + y = 4$
Subtract $\dfrac{69}{14}$ from both sides of the equation to isolate constants to the right side of the equation:
$y = 4 - \dfrac{69}{14}$
Convert $4$ into a fraction with $14$ as the denominator:
$y = \dfrac{56}{14} - \dfrac{69}{14}$
$y = -\dfrac{13}{14}$
The solution is $\left(\dfrac{23}{14}, -\dfrac{13}{14}\right)$.
