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Chapter 11: Q. 39 (page 794)

In Problems 39鈥�43, solve each system of equations.

2x+y+3=0x2+y2=5

Short Answer

Expert verified

Solutions of the system of equations2x+y+3=0x2+y2=5 are-25,-115&-2,1

Step by step solution

01

Step 1. Given data

The given system of equation is

2x+y+3=0x2+y2=5

02

Step 2. Formation of the single-variable equation

Rearrange equation 2x+y+3=0

2x+y+3=0y=-2x-3

Substitute expression of y in equation x2+y2=5

x2+y2=5x2+(-2x-3)2=5 5x2+12x+9=5

03

Step 3. Solution of the single variable equation

Use the quadratic formula to solve 5x2+12x+9=5

role="math" localid="1646946851981" x=-b卤b2-4ac2ax=-12卤122-4(5)(9)2(5)x=-12卤810

Separate the solutions

x=-12+810x=-25

and

x=-12-810x=-2

04

Step 4. Solution of the system of equations

Substitute x=-25in equation role="math" localid="1646947083975" y=-2x-3

role="math" y=-2x-3y=-2-210-3y=45-3y=-115

Substitute x=-2in equationy=-2x-3

y=-2x-3y=-2-2-3y=1

So solutions of the system of equations are-25,-115&-2,1

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Most popular questions from this chapter

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