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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 11.76 (page 1144)

Solve the system by elimination.
$x^{2} + y^{2} = 4 x^{2} - y^{2} = 4$

Short Answer

Expert verified

The solution of the system is $(- 2, 0), (2, 0)$ .

Step by step solution

01

Step 1. Given information

The given equations are $x^{2} + y^{2} = 4 x^{2} - y^{2} = 4$ .

02

Step 2. Add the equations

Both the equations are in standard form. The sign of $y^{2}$ is opposite in the equations. Add them to eliminate $y^{2}$ .

$\begin{array}{rcl} x^{2} + y^{2} + x^{2} - y^{2} & = & 4 + 4 \\ 2 x^{2} & = & 8 \end{array}$

03

Step 3. Find x

Use the obtained equation to find the value of x.

$\begin{array}{rcl} 2 x^{2} & = & 8 \\ x^{2} & = & 4 \\ x & = & 卤 2 \end{array}$

04

Step 4. Find y

Substitute $x^{2} = 4$ in one of the given equations and solve for y.

$\begin{array}{rcl} 4 + y^{2} & = & 4 \\ y^{2} & = & 0 \\ y & = & 0 \end{array}$

So, the solution of the system is $(- 2, 0), (2, 0)$ .

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