Chapter 11: Q. 13 (page 772)

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.
$x^{2} + y^{2} = 4; x^{2} + 2 x + y^{2} = 0$

Short Answer

Expert verified

The graph of the system of equations $x^{2} + y^{2} = 4; x^{2} + 2 x + y^{2} = 0$ is:

Step by step solution

Step 1. Given

The system of non-linear equation:

$x^{2} + y^{2} = 4; x^{2} + 2 x + y^{2} = 0$

To graph the equation and to find the point of intersection.

Step 2. Graph the equations

Graph the equations in the same plane.

Step 3. To find the point of intersection.

Substitute the first equation in second equation,

$x^{2} + y^{2} + 2 x = 0 4 + 2 x = 0 2 x = - 4 x = - 2$

Step 4. Find y

Substitute $x = - 2$ in the equation,

$x^{2} + y^{2} = 4 {(- 2)}^{2} + y^{2} = 4 4 + y^{2} = 4 y^{2} = 0 y = 0$

The point of intersection is $(- 2, 0)$

Step 5. Plot the point of intersection

The graph of the system of non-linear equations with the point of intersection is:

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In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.
$x^{2} + y^{2} = 4; x^{2} + 2 x + y^{2} = 0$

Short Answer

Step by step solution

Step 1. Given

Step 2. Graph the equations

Step 3. To find the point of intersection.

Step 4. Find y

Step 5. Plot the point of intersection

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In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.x2+y2=4;x2+2x+y2=0

Short Answer

Step by step solution

Step 1. Given

Step 2. Graph the equations

Step 3. To find the point of intersection.

Step 4. Find y

Step 5. Plot the point of intersection

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Applied Mathematics

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.
$x^{2} + y^{2} = 4; x^{2} + 2 x + y^{2} = 0$