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Chapter 11: Q. 11.69 (page 1140)

Solve the system by using substitution:

x2+9y2=9y=13x-3

Short Answer

Expert verified

The given system has no solution

Step by step solution

01

Step 1. Given Information

The given system isx2+9y2=9y=13x-3.

02

Step 2. Solution of x

  • Substitute y=13x-3into x2+9y2=9and simplify.

role="math" localid="1645614043008" x2+9(13x-3)2=9x2+9(x29+9-2x)=9x2+x2+81-18x=92x2-18x+72=0x2-9x+36=0

  • In the obtained equation (-9)2-4(1)(36)=-63<0, so the equation does not have real roots.
  • Since no real value of xexists, the given system has no solution.

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