Q51. - Algebra 2

Question

Solve each system of equations.

 

 $\begin{array}{c}r+s+t=15\\ r+t=12\\ s+t=10\end{array}$

Step-by-Step Solution

Answer

The solution of the system of equations: $\begin{array}{c}r+s+t=15\\ r+t=12\\ s+t=10\end{array}$  is $\left(5,3,7\right)$. 

Step 1 - Solve for variable s

Let the equations be:

 

$r+s+t=15$             … (i)

$r+t=12$               … (ii)

$s+t=10$               … (iii) 

 

Substitute 12 for $r+t$ into equation (i) and solve for s.

$\begin{array}{c}r+s+t=15\\ s+\left(r+t\right)=15\\ s+12=15\\ s+12-12=15-12\\ s=3\end{array}$

Step 2 - Solve for variable t

Substitute 3 for s into equation (iii) so as to obtain the value of t.

$\begin{array}{c}3+t=10\\ 3+t-3=10-3\\ t=7\end{array}$

Step 3 - Solve for variable r

Now substitute 7 for t into the equation (ii) so as to obtain variable r. 

$\begin{array}{c}r+7=12\\ r+7-7=12-7\\ r=5\end{array}$

Therefore, the solution $\left(r,s,t\right)$ is $\left(5,3,7\right)$.