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.

$\begin{array}{l}2x-3y=-8\\ 14x-21y=3\end{array}$

Short answer

Hence, the solution of the system of equations $\begin{array}{l}2x-3y=-8\\ 14x-21y=3\end{array}$has no solution henceinconsistent.

Step-by-step solution

Step 1. Given information.

Given a system of equations$\begin{array}{l}2x-3y=-8\\ 14x-21y=3\end{array}$

substitution method.

Step 2. Write down the concept.

Given equation,

$2x-3y=-8$ …….(1)

$14x-21y=3$ …….(2)

We are solving equation (1) for x,

$x=-\frac{1}{2}\left(-8+3y\right)$ ……..(3)

Step 3. Determining the angle

We are substituting equation (3) in equation (2),

$\begin{array}{l}14\left(-4+\frac{3}{2}y\right)-21y=3\\ -56+21y-21y=3\end{array}$

Adding $56$ on both sides,

$0=59$

Since, this is false so the system is inconsistent, i.e. no solution.