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Q12.

Expert-verifiedFound in: Page 688

Book edition
7th Edition

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

Pages
948 pages

ISBN
9781337067508

**Elimination Method**

**Use the elimination method to find all solutions of the system of equations.**

**$\left\{\begin{array}{l}2x-5y=-18\\ 3x+4y=19\end{array}\right.$**

Hence, all solutions of the system of equations are $x=1\&y=4$

We are given the system of linear equations that is-

$\left\{\begin{array}{l}2x-5y=-18\\ 3x+4y=19\end{array}\right.$

The system of linear equations is the collection of one or more linear equations involving the same set of variables.

We need to find all solutions to the system of equations.

By the Elimination Method, we will calculate the result.

We multiply the first equation by $2$ and add the second equation to it to eliminate the *x* term.

$\begin{array}{l}3\times [2x-5y=-18]\\ 6x-15y=-54\\ 2\times 3x+4y=19\\ 6x+8y=38\end{array}$

Further solving,

$\begin{array}{l}(6x-6x)+(-15y-8y)=-54-38\\ -23y=-92\\ y=4\end{array}$

We substitute the value of *y* in any of the original equations to get back the value of *x*

$\begin{array}{l}3x+4\times 4=19\\ 3x+16=19\\ 3x=3\\ x=1\end{array}$

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