Question

incorrect
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use elimination to solve the system of equations.
6r - 6t = 6
3r - 6t = 15
( , )
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Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases} 6r - 6t = 6 \\ 3r - 6t = 15 \end{cases}$$

Subtract the second equation from the first equation to eliminate \(t\):
\((6r - 6t)-(3r - 6t)=6 - 15\)
Simplify the left - hand side: \(6r-6t - 3r + 6t=3r\)
Simplify the right - hand side: \(6 - 15=-9\)
So we get \(3r=-9\)

Step2: Solve for \(r\)

Divide both sides of the equation \(3r = - 9\) by 3:
\(r=\frac{-9}{3}=-3\)

Step3: Substitute \(r\) into one of the original equations

Substitute \(r = - 3\) into the first equation \(6r-6t = 6\):
\(6\times(-3)-6t = 6\)
Calculate \(6\times(-3)=-18\), so the equation becomes \(-18-6t = 6\)
Add 18 to both sides: \(-6t=6 + 18\)
\(-6t=24\)
Divide both sides by - 6: \(t=\frac{24}{-6}=-4\)

Answer:

\((-3,-4)\)