Answer
The solution to this system of equations is $(-3, -\frac{23}{4})$.
Work Step by Step
First, we rewrite the second equation so that the variables are on one side while the constant is on the other. We need to subtract $14$ from each side of the equation to move the constant to the right side of the equation:
$4t = 3c - 14$
To move all variables to the left side of the equation, we subtract $3c$ from each side of the equation:
$-3c + 4t = -14$
We see that in the two equations, the $t$ terms are exactly the same except they have opposite signs. If we add these two equations together, we can eliminate the variable $t$ and just deal with one variable instead of two:
Let us combine the two equations together:
$ 5c - 4t = 8$
$-3c + 4t = -14$
Let us add the equations together:
$(5c-4t)+(-3c+4t)=8+(-14)\\
2c = -6$
Divide each side by $2$ to solve for $c$:
$c = -3$
Now that we have the value for $c$, we can plug it into one of the equations to solve for $t$.
Let us plug in the value for $c$ into the first equation:
$5c-4t=8\\
5(-3) - 4t = 8$
$-15 - 4t = 8$
Now, we add $15$ to both sides of the equation to isolate constants to the right side of the equation:
$-4t = 23$
Divide both sides by $-4$ to solve for $t$:
$t = -\frac{23}{4}$
The solution to this system of equations is $(-3, -\frac{23}{4})$.
