Systems of equations
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Systems of equations. Chapter 8. 8.1 – solving systems of equations graphically. Chapter 8. Systems of equations. If you have a system of equations , you can solve it by graphing both equations. . Consider if you were given one quadratic equation and one linear equation:.

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Systems of equations

Systems of equations

Chapter 8


8 1 solving systems of equations graphically

8.1 – solving systems of equations graphically

Chapter 8


Systems of equations1

Systems of equations

If you have a system of equations, you can solve it by graphing both equations.

Consider if you were given one quadratic equation and one linear equation:

Consider if you were given two quadratic equations:


Example

example

Solve the following system of equations graphically:

4x – y + 3 = 0

2x2 + 8x – y + 3 = 0

If we want to graph the equations, what do we need to solve for in each equation?

To find the intersection points use

TRACE  INTERSECT

4x – y + 3 = 0

 4x + 3 = y

2x2 + 8x – y + 3 = 0

 2x2 + 8x + 3 = y

Points of intersection are (0, 3) and (–2, –5)


Try it

Try it

Solve the system graphically, and verify your solution:

x – y + 1 = 0

x2 – 6x + y + 3 = 0


Example1

example

Solve:

2x2 – 16x – y = –35

2x2 – 8x – y = –11

  • 2x2 – 16x – y = –35

  • 2x2 – 16x + 35 = y

2x2 – 8x – y = –11

 2x2 – 8x + 11 = y

The intersection point is at (3, 5).


Example2

example

Suppose that in one stunt, two Cirque du Soleil performers are launched toward each other from two slightly offset seesaws. The first performer is launched, and 1 s later the second performer is launched in the opposite direction. They both perform a flip and give each other a high five in the air. Each performer is in the air for 2 s. The height about the seesaw versus time for each performer during the stunt is approximated by the parabola as shown. Their paths are shown on a coordinate grid.

Determine the system of

equations that models their

height during the stunt.

b) Solve the system.


Example3

example


Pg 435 439 3 4 5 6 8 9 11 13

Pg. 435–439, # 3, 4, 5, 6, 8, 9, 11, 13.

Independent Practice


7 2 solving quadratic equations by factoring

7.2 – solving quadratic equations by factoring

Chapter 7


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