Question

Solve each system of equations.

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

Short 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-by-step solution

- 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.

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

- Solve for variable t

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

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

- 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 $\left(5,3,7\right)$.