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Expert-verified Found in: Page 149 ### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903 # Solve each system of inequalities by graphing.$\begin{array}{c}y\ge x-3\\ y\ge -x+1\end{array}$

The solution of the inequalities is$-y+1\le x\le y+3$.

See the step by step solution

## Step-1 – Concept of solution of linear inequalities

The solution of linear inequalities can be obtained by changing the inequalities into equations and solving the linear equations to obtain a graph. Then the common shaded region is a solution of the inequalities.

## Step-2 – Concept of shading the region of the inequalities

The shaded region obtained by choosing a point, if the point satisfies the inequality the region is along the point, if not satisfies the inequalities, then the shaded region is opposite to the point.

## Step-3 – Solving the inequalities

The given inequalities are-:

$\begin{array}{c}y\ge x-3\\ y\ge -x+1\end{array}$

The linear equation of the inequalities is-:

$\begin{array}{c}y=x-3\\ y=-x+1\end{array}$

The point which satisfies the equation $y=x-3$ are $\left(0,-3\right)$and$\left(3,0\right)$.

The point which satisfies the equation $y=-x+1$ are $\left(0,1\right)$ and$\left(1,0\right)$.

## Step-4 – Evaluating the shading region

We choose $\left(0,0\right)$then the point $\left(0,0\right)$ satisfies the inequality $y\ge x-3$ but it does not satisfy the inequality $y\ge -x+1$.

## Step-5 – Plotting the graph

So, the graph of the inequality is The common region is $-y+1\le x\le y+3$ ### Want to see more solutions like these? 