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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

# The following is a system of two linear equations in two variables. $\left\{\begin{array}{l}x+y=1\\ 2x+2y=2\end{array}\right\$The graph of the first equation is the same as the graph of the second equation, so the system has _______ _______solutions. We express these solutions by writing $\begin{array}{l}x=t\\ y=______\end{array}$where $t$ is any real number. Some of the solutions of this system are $\left(1,___\right),\left(-3,___\right)$ and $\left(5,___\right)$

Infinitely many solutions, $y=1-t$ and $\left(1,0\right),\left(-3,4\right)&\left(5,-4\right)$

See the step by step solution

## Step 1. Given information

In this question, we have been given a sentence.

## 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 complete the given sentence.

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

## Step 3. Calculation

We know that the following is a system of linear equations in two variables,

$\left\{\begin{array}{l}x+y=1\\ 2x+2y=2\end{array}\right\$

The graph of the first equation is the same as the second equation, so the system has infinitely many solutions. We express the solutions by writing

$\begin{array}{l}x=t\\ y=1-t\end{array}$

Where t is any real number. Some of the solutions of this system are $\left(1,0\right),\left(-3,4\right)&\left(5,-4\right)$