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Chapter 11: Q. 41 (page 794)

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

x2+y2=6yx2=3y

Short Answer

Expert verified

Solutions of the system of equationsx2+y2=6yx2=3y are(0,0),(-3,3),&(3,3)

Step by step solution

01

Step 1. Given data 

The given system of equation is

x2+y2=6yx2=3y

02

Step 2. Formation of the single-variable equation 

Substitute x2=3yin equation x2+y2=6y

x2+y2=6y3y+y2=6yy2-3y=0y(y-3)=0

03

Step 3. Solution of the single variable equation 

Use zero product property for y(y-3)=0

y-3=0y=3

andy=0

04

Step 4. Solution of the system of equations 

Substitute y=0in equationx2=3y

x2=3yx2=3(0)x2=0x=0

Substitute role="math" localid="1646948862177" y=3in equationx2=3y

x2=3yx2=33x2=9x=卤3

So solutions of the system of equations are(0,0),(-3,3),&(3,3)

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