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Q40.

Expert-verifiedFound in: Page 689

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**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.**

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

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

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

substitution method.

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)

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.

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