Answer
The solution to this system of equations is $r = -6$ and $t = -9$.
Work Step by Step
In the first equation, we already have an expression for $t$ that we can substitute into the second equation to find $r$. Let us do the substitution:
$5r - 4(2r + 3) = 6$
Use distributive property to get rid of the parentheses:
$5r - 8r - 12 = 6$
Add $12$ to both sides to isolate constants to the right side of the equation:
$5r - 8r = 18$
Add like terms on the left side to simplify:
$-3r = 18$
Divide each side by $-3$ to solve for $r$:
$r = -6$
Now that we have a value for $r$, we can substitute it into the first equation to solve for $t$:
$t = 2(-6) + 3$
$t = -12 + 3$
$t = -9$
The solution to this system of equations is $r = -6$ and $t = -9$.
Let us substitute these values into the second equation to see if the equation holds true:
$5(-6) - 4(-9) = 6$
$-30 + 36 = 6$
$6 = 6$
This statement is true; therefore, the solution is correct.
