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Chapter 11: Q. 11.72 (page 1141)

Solve the system by using substitution:

y2-x=0y=3x-2

Short Answer

Expert verified

The solutions of the system are(1,1),49,-23.

Step by step solution

01

Step 1. Given information

The given system isy2-x=0y=3x-2.

02

Step 2. Substitution 

  • Find the value of xfrom y2-x=0.

x=y2

  • Substitute x=y2into y=3x-2and simplify.

role="math" localid="1645787646995" y=3y2-23y2-y-2=03y2-3y+2y-2=0(y-1)(3y+2)=0

  • So,y=1,-23
03

Step 3. Solve for x

  • Substitute y=1into y2-x=0 and solve for x.

1-x=0x=1

  • Substitute y=-23into the same equation and solve.

49-x=0x=49

  • So, the solutions of the system are(1,1),49,-23

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