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What is a System of Equations?PowerPoint Presentation

What is a System of Equations?

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What is a System of Equations?

- Use the iPads to find information about:
- Uses
- Ways to solve
- Real-world applications
- Types
- Vocabulary

Can you look at a system of linear equations and tell how many solutions it has?

For example:

Could you tell that the equations y=2x +1 and y= 2x-7 have no solution?

In this lesson you many solutions it has?will learn to predict how many solutions a system of linear equations has by inspection.

y = 2x + 1 many solutions it has?

Assuming that many solutions it has?all equations have one solution because those are the types of equations that are solved the most.

There are three types of solutions for systems of linear equations

One None Infinitely Many

y = equationsx - 5

y = 4x +4

y = 2x + 1

y = x - 3

y = 4(x+1)

y = 3x + 1

Same Line infinitely many solutions

Parallel lines no solution

One point

one solution

Determine the number of solutions that the system has. equations

Slope: -4, y-intercept: -16

y = -4(x+4)

y = -4x-16

Slope: -4, y-intercept: -16

y = -4x-16

Determine the number of solutions that the system has. equations

Slope: 1, y-intercept: 1

y = x + 1

Slope: , y-intercept: 1

y = x + 1

Determine the number of solutions that the system has. equations

Slope: -5, y-intercept: 1

y = -5x + 1

Slope: -5, y-intercept: -2

y = -5x-2

- Create a second equation for the following system of equations so that they have one solution, no solution, and infinitely many solutions.

- One solution

- y = 7x + 1 y=

- No solution

- y = 7x + 1 y=

- Infinitely many solutions

- y = 7x + 1 y=

How many solutions does the system of equations have? y=6(x+1) and y=6x+6

a) One b) None c) Infinitely Many

How many solutions does the system of equations have? y=-3x and y=x+1

a) One b) None c) Infinitely Many

Not having the equation in slope- intercept form intersect?

y = 2 -x

3x + 2y = 4

y = -x + 2

-3x = -3x

2y = 4 -3x

Slope: -, y-intercept: 2

2 = 2

Graph the system of linear equations. Determine their solution.

y = x-1

y -2x = 2

+2x = +2x

y = 2 + 2x

y = 2x + 2

Graph the system of linear equations. Determine their solution.

Slope: 1, y-intercept: -1

y = x-1

Slope: 2, y-intercept: -2

y = 2x-2

Graph the system of linear equations. Determine their solution.

y = x+3

-4x + y = 0

+4x = +4x

y = 4x

Graph the system of linear equations. Determine their solution.

Slope: 4, y-intercept: 0

y = 4x

Slope: 1, y-intercept: 3

y = x+3

- When we solve the systems of equations y=2x and y=x, what is our solution? What does it mean?

- How many solutions does the system of equations y=2x+1 and y=x+1 have? Why?

The solution for the system of linear equations y=3x+4 and y=x+2 is?

a) (-1,1) b) (1,-1) c)(-1,-1) d) (1,1)

The solution for the system of linear equations y=x+6 and y=-2x is?

a) (2,-4) b) (-2,4) c) (-2,-4) d) (2,4)

Graph the system of linear equations. Determine their solution.

y - 4 = 2x

y = 2x

+ 4 = + 4

y = 2x + 4

Graph the system of linear equations. Determine their solution.

Slope: 2, y-intercept: 0

y = 2x

Slope: 2, y-intercept: 4

y = 2x+4

y = 2x solution.

y = 2x+4

Graph the system of linear equations. Determine their solution.

-x + 2y = 0

2y –x = - 2

+x = +x

+x = +x

2y = x - 2

2y = x

2 = 2

2 = 2

y = x- 1

y = x

Graph the system of linear equations. Determine their solution.

Slope: , y-intercept: 0

y = x

Slope: , y-intercept: -1

y = x- 1

y = solution.x

y = x- 1

y = solution. x

y = x- 1

Find the solution for the system of linear equations y=3x and y=3x-2 by graphing.

The solution for the system of linear equations y=2x+1 and y=2x-3 is?

a) (-1,1) b) (1,-1) c)(-1,-1) d) no solution

The solution for the system of linear equations y=-x+6 and y=-x-2 is?

a) (2,-4) b) (-2,4) c) (-2,-4) d) no solution

Graph the system of linear equations. Determine their solution.

y = 2(2x+4)

y – 4x = 8

y = 4x+8

+4x = +4x

y = 4x + 8

Graph the system of linear equations. Determine their solution.

Slope: 4, y-intercept: 8

y = 2(2x+4)

y = 4x+8

Slope: 4, y-intercept: 8

y = 4x+8

Graph the system of linear equations. Determine their solution.

x -y = -1

y =x-2+3

-x =-x

y =x+1

-y = -1-x

-1 = -1

y= 1 +x

y= x + 1

Graph the system of linear equations. Determine their solution.

Slope:1, y-intercept: 1

y =x+1

Slope:1, y-intercept: 1

y =x-2+3

y =x+1

y-3x = 3 solution.

y =3(x+1)

The solution for the system of linear equations y=2x+1 and y=2x-3 is?

a) One solution b)Infinitely Many Solutions

The solution for the system of linear equations y=4x-12and y=4(x+3)is?

a) One solution b) Infinitely Many Solutions

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