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Chapter 11: Q. 8 (page 772)

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

y=4-x2;y=2x+4

Short Answer

Expert verified

he graph of the system of equations y=4-x2;y=2x+4is:

The points of intersection are (-65,85),(-2,0)

Step by step solution

01

Step 1. Given

The system of non-linear equation:

y=4-x2;y=2x+4

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

02

Step 2. Graph the equations

Graph the equations in the same plane.

03

Step 3. To find the point of intersection.

Equate both the equations,

4-x2=2x+4

Squaring on both sides, we get,

4-x2=(2x+4)24-x2=4x2+16x+165x2+16x+12=0

04

Step 4. Solve the equations

5x2+16x+12=0(5x+6)(x+2)=0x=-65,-2

The value of x is -65,-2

05

Step 5. Find y

When

x=-65,y=2x+4=2(-65)+4=-125+4=85

When x=-2,

y=2x+4=2(-2)+4=0

The point of intersections are (-65,85),(-2,0)

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Most popular questions from this chapter

Solve each system of equations. If the system has no solution, say that it is inconsistent.

x-2y+3z=72x+y+z=4-3x+2y-2z=-10

solve each system of equations. If the system has no solution, say that it is inconsistent

x + 4y - 3z = -8

3x - y + 3z = 12

x + y + 6z = 1

Graph the equation:x2+4y2=4

Solve each system of equations. If the system has no solution, say that it is inconsistent.
x+3y=52x-3y=-8

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

x2+y2=10;y=x+2
See all solutions

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