Q53. - Algebra 2

Question

Solve each system by using substitution or elimination.

 

 $\begin{array}{c}2s+7t=39\\ 5s-t=5\end{array}$

Step-by-Step Solution

Answer

The solution of the system of equations:  $\begin{array}{c}2s+7t=39\\ 5s-t=5\end{array}$ is $\left(2,5\right)$. 

Step 1 - Solve the second equation for t in terms of s

Write the equation $5s-t=5$ in terms of t.

 

$\begin{array}{c}5s-t=5\\ 5s-t-5s=5-5s\\ -t\times \left(-1\right)=\left(5-5s\right)\times \left(-1\right)\\ t=5s-5\end{array}$

Step 2 - Solve for s

Substitute $5s-5$ for t into equation $2s+7t=39$ so as to obtain the value of s.

 

$\begin{array}{c}2s+7\left(5s-5\right)=39\\ 2s+7\left(5s\right)-7\left(5\right)=39\\ 2s+35s-35=39\\ 37s-35+35=39+35\\ 37s=74\\ s=2\end{array}$

Step 3 - Solve for t

Now substitute 2 for s into either original equation and solve for t. 

$\begin{array}{c}2\left(2\right)+7t=39\\ 4+7t-4=39-4\\ 7t=35\\ t=5\end{array}$

Therefore, the solution of the system is $\left(2,5\right)$.