Chapter 11: Q. 17 (page 772)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given

The system of non-linear equation:

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

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 second equation in the first equation,

${(y^{2} - 4)}^{2} + y^{2} = 4; y^{4} - 8 y^{2} + 16 + y^{2} = 4 y^{4} - 7 y^{2} + 12 = 0$

Step 4. Solve the equation

$y^{4} - 7 y^{2} + 12 = 0 (y^{2} - 4) (y^{2} - 3) = 0 y^{2} = 3, 4 y = \pm \sqrt{3}, \pm 2$

Step 5. Find x

When $y = \pm \sqrt{3}$ ,

$x^{2} + {(\pm \sqrt{3})}^{2} = 4 x^{2} + 3 = 4 x^{2} = 1 x = \pm 1$

When $y = \pm 2$ ,

$x^{2} + {(\pm 2)}^{2} = 4 x^{2} + 4 = 4 x^{2} = 0 x = 0$

The points of intersection are $(- 1, - \sqrt{3}) (- 1, \sqrt{3}), (0, - 2), (0, 2)$

Step 6. 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.
$x^{2} + y^{2} = 4; y^{2} - x = 4$

Short Answer

Step by step solution

Step 1. Given

Step 2. Graph the equations

Step 3. To find the point of intersection.

Step 4. Solve the equation

Step 5. Find x

Step 6. 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;y2-x=4

Short Answer

Step by step solution

Step 1. Given

Step 2. Graph the equations

Step 3. To find the point of intersection.

Step 4. Solve the equation

Step 5. Find x

Step 6. Plot the point of intersection

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Statistics

Mechanics Maths

Calculus

Theoretical and Mathematical Physics

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.
$x^{2} + y^{2} = 4; y^{2} - x = 4$