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Expert-verified Found in: Page 688 ### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508 # Elimination MethodUse 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 $x=1&y=4$

See the step by step solution

## Step 1. Given information

We are given the system of linear equations that is-

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

## Step 2. Concept used

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.

## Step 3. Calculation

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

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

Further solving,

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

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

$\begin{array}{l}3x+4×4=19\\ 3x+16=19\\ 3x=3\\ x=1\end{array}$ ### Want to see more solutions like these? 