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Q13.

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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

# Graphical MethodTwo equations and their graphs are given. Find the intersection point(s) of the graphs by solving the system.$\left\{\begin{array}{l}2x+y=-1\\ x-2y=-8\end{array}\right\$

Hence, the intersection points of the graphs by solving the system are $x=-2&y=3$

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+y=-1\\ x-2y=-8\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 the intersection points of the graphs by solving the system. By the Graphical Method, we will calculate the result.

## Step 3. Calculation

We multiply the first equation by $2$ and add the second equation to eliminate the $y$

$\begin{array}{l}2×\left[2x+y=-1\right]\\ 4x+2y=-2\\ x-2y=-8\end{array}$

Further solving,

$\begin{array}{l}\left(4x+x\right)\\ 5x=-10\\ x=-2\end{array}$

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

$\begin{array}{l}-2-2y=-8\\ 2y=8-2\\ 2y=6\\ y=3\end{array}$