Question

Solve the system, or show that it has no solution. If the system has infinitely many solutions,

express them in the ordered-pair form given in Example 6.

$\begin{array}{l}8s-3t=-3\\ 5s-2t=-1\end{array}$

Short answer

Hence, the solution of the system of equations $\begin{array}{l}8s-3t=-3\\ 5s-2t=-1\end{array}$has the ordered pair $\left(-3,-7\right)$.

Step-by-step solution

Step 1. Given information.

Given a system of equations$\begin{array}{l}8s-3t=-3\\ 5s-2t=-1\end{array}$

substitution method.

Step 2. Write down the concept.

Given equation,

$8s-3t=-3$ …….(1)

$5s-2t=-1$ …….(2)

Multiplying equation (1) for s,

$s=\frac{1}{8}\left(-3+3t\right)$ ……..(3)

Step 3. Determining the angle

Substituting equation (3) in equation (2),

$\begin{array}{l}5\left(\frac{-3}{8}+\frac{3}{8}t\right)-2t=-1\\ \frac{-15}{8}+\frac{15}{8}t-2t=-1\end{array}$

Adding $\frac{15}{8}$ on both sides,

$\frac{-t}{8}=\frac{7}{8}$

Multiplying both sides by -8

$t=-7$

Substituting back value of t in equation (3)

$\begin{array}{l}s=\frac{-3}{8}+\frac{3}{8}(-7)\\ s=\frac{-3}{8}-\frac{21}{8}\\ s=\frac{-24}{8}\\ s=-3\end{array}$