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Algebra 2
Found in: Page 149
Algebra 2

Algebra 2

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

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Short Answer

12: Solve each system of inequalities by graphing.


The solution of the inequalities is 2y+3x<-5-y3.

See the step by step solution

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-:


The linear equation of the inequalities is-:


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

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

Step-4 – Evaluating the shading region

We choose the point (0,0). The point which (0,0)does not satisfy any of the inequalities 3x+y<-5 and 2x-4y6.

Step-5 – Plotting the graph

So, the graph of the inequality is

The common shaded region is2y+3x<-5-y3.

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