Answer
The solution to this system of equations is $(\frac{5}{2}, 2)$.
Work Step by Step
First, we rewrite the equations so that the variables are on one side while the constant is on the other:
For the first equation, we subtract $11$ from each side of the equation to shift constants to one side of the equation:
$-2c = 3d - 11$
Subtract $3d$ from both sides of the equation to move all variables to the left side of the equation:
$-2c - 3d = -11$
We now can see that in the two equations, the $c$ terms are exactly the same except they have opposite signs. If we add these two equations together, we can eliminate the variable $c$ and just deal with one variable instead of two.
Let us combine the two equations:
$-2c - 3d = -11$
$ 2c - 7d = -9$
Let us add the two equations together to come up with a single equation:
$-10d = -20$
Divide each side by $-10$ to solve for $d$:
$d = 2$
Now that we have the value for $d$, we can plug it into one of the equations to solve for $c$.
Let us plug in the value for $d$ into the first equation:
$11 - 2c = 3(2)$
$11 - 2c = 6$
Now, we subtract $11$ from both sides of the equation to isolate constants to the right side of the equation:
$- 2c = -5$
Divide both sides by $-2$ to solve for $c$:
$c = \frac{5}{2}$
The solution to this system of equations is $(\frac{5}{2}, 2)$.
