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Chapter 11: Q. 11.75 (page 1144)

Solve the system by elimination

x2+y2=25y2-x2=7

Short Answer

Expert verified

The solutions of the system are(3,4),(-3,4),(3,-4),and(-3,-4).

Step by step solution

01

Step 1. given information

The given system isx2+y2=25y2-x2=7.

02

Step 2. Add the Equations

  • As the sign of x2is opposite in both the equations, add them to eliminate x2.

x2+y2-x2+y2=25+72y2=32

03

Step 3. Find y

  • From the obtained equation, find the value of y.

y2=16y=卤4

04

Step 4. Find x

  • Substitute y2=16 in one of the given equation and find x.

16-x2=7x2=9x=卤3

  • So, the solutions of the system arerole="math" localid="1645515344360" (3,4),(-3,4),(3,-4),and(-3,-4).

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