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### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

# Number of SolutionsDetermined Graphically Graph each linear system, either by hand or using a graphing device. Use the graph to determine whether the system has one solution, no solution, or infinitely many solutions. If there is exactly one solution, use the graph to find it.$\left\{\begin{array}{l}-x+\frac{1}{2}y=-5\\ 2x-y=10\end{array}\right\$

Hence, the system of linear equations has infinitely many solutions and the sketch of the graph is.

See the step by step solution

## Step 1. Given information

We are given the system of linear equations that is-

$\left\{\begin{array}{l}-x+\frac{1}{2}y=-5\\ 2x-y=10\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 use the graph to determine whether the system has one solution, no solution, or infinitely many solutions.

By the process of the system of equations, we will calculate the result.

## Step 3. Calculation

Two lines indicated correspond to the two equations from the system of linear equations.

As is evident by the graphs, the two lines are overlapping and each point on either of the lines can be considered an intersection.

So, We can conclude that the system of linear equations has infinitely many solutions.

We sketch the graph,