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Q12.

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Found in: Page 149

### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

# 12: Solve each system of inequalities by graphing.$\begin{array}{c}3x+y<-5\\ 2x-4y\ge 6\end{array}$

The solution of the inequalities is $2y+3\le x<\frac{-5-y}{3}$.

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-:

$\begin{array}{c}3x+y<-5\\ 2x-4y\ge 6\end{array}$

The linear equation of the inequalities is-:

$\begin{array}{c}3x+y=-5\\ 2x-4y=6\end{array}$

The point which satisfies the equation $3x+y=-5$are $\left(0,5\right)$ and$\left(2,-1\right)$.

The point which satisfies the equation $2x-4y=6$ are $\left(3,0\right)$ and$\left(1,-1\right)$.

## Step-4 – Evaluating the shading region

We choose the point $\left(0,0\right)$. The point which $\left(0,0\right)$does not satisfy any of the inequalities $3x+y<-5$ and $2x-4y\ge 6$.

## Step-5 – Plotting the graph

So, the graph of the inequality is

The common shaded region is$2y+3\le x<\frac{-5-y}{3}$.