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Chapter 4: Q 4.106 (page 461)

Determine whether the ordered pair is the solution to the system: y>4x-24x-y<20

a)(-2,1)

b)(4,-1)

Short Answer

Expert verified

The ordered pair (-2,1)is a solution to the system of inequalities y>4x-24x-y<20

And the ordered pair (4,-1) is not a solution to the system of inequalities y>4x-24x-y<20

Step by step solution

01

Part a) Step 1. Given

The system of inequalities, y>4x-24x-y<20

(x,y)=(-2,1)

(x,y)=(4,-1)

02

Part a) Step 2. Substitute the points in the first equation

Substitute the point (-2,1)in the system of inequalities.

y>4x-2

(1)>4(-2)-2

1>-10 holds true.

03

Part a) Step 3. Substitute the points in the second equation

Substitute the point (-2,1)in the system of inequalities.

4x-y<20

localid="1644484036783" 4(-2)-(1)<20

-9<20holds true.

The ordered pair (-2,1)made both the inequality true.

Therefore, (-2,1)is a solution to this system.

04

Part b) Step 1. Substitute the points in the first equation

Substitute the point (4,-1)in the system of inequality

y>4x-2

(-1)>4(4)-2

-1>14 is false

05

Part b) Step 2. Substitute the points in the second equation

Substitute the point (4,-1)in the system of inequalities.

4x-y<20

4(4)-(-1)<20

16+1<20

17<20is true

The ordered pair (4,-1)made one inequality true, but the other one is false.

Therefore, (4,-1)is not a solution to this system.

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