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# What is a System of Equations? - PowerPoint PPT Presentation

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:

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• 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.

Slope Intercept Form of an Equation many solutions it has?

y = mx + b

slope

y-intercept

Graphing a linear equation many solutions it has?

y = 2x + 1

slope

y-intercept

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.

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

Slope: -4, y-intercept: -16

y = -4(x+4)

y = -4x-16

Slope: -4, y-intercept: -16

y = -4x-16

Slope: 1, y-intercept: 1

y = x + 1

Slope: , y-intercept: 1

y = x + 1

Slope: -5, y-intercept: 1

y = -5x + 1

Slope: -5, y-intercept: -2

y = -5x-2

y= -2x+1

y= -2x-2

y= -3x+1

y= -2x-7

y= -3(x+1)

y= -3x-3

• 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

y = x-1

y = 2x-2

y = 2 -x

3x + 2y = 4

y = -x + 2

-3x = -3x

2y = 4 -3x

Slope: -, y-intercept: 2

2 = 2

y = x-1

y -2x = 2

+2x = +2x

y = 2 + 2x

y = 2x + 2

Slope: 1, y-intercept: -1

y = x-1

Slope: 2, y-intercept: -2

y = 2x-2

y = x-1 solution.

0 = 1-1

0 = 0

(1,0)

y = 2x-2

0 = 2*1-2

0 = 0

y = x+3

-4x + y = 0

+4x = +4x

y = 4x

Slope: 4, y-intercept: 0

y = 4x

Slope: 1, y-intercept: 3

y = x+3

y = 4x solution.

4 = 4*1

(1,4)

4 = 4

y = x+3

4 = 1+3

4 = 4

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)

y = x

y = x- 1

y - 4 = 2x

y = 2x

+ 4 = + 4

y = 2x + 4

Slope: 2, y-intercept: 0

y = 2x

Slope: 2, y-intercept: 4

y = 2x+4

y = 2x solution.

y = 2x+4

-x + 2y = 0

2y –x = - 2

+x = +x

+x = +x

2y = x - 2

2y = x

2 = 2

2 = 2

y = x- 1

y = x

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

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

y = 2(2x+4)

y = 4x+8

y = 2(2x+4)

y – 4x = 8

y = 4x+8

+4x = +4x

y = 4x + 8

Slope: 4, y-intercept: 8

y = 2(2x+4)

y = 4x+8

Slope: 4, y-intercept: 8

y = 4x+8

y = 2(2x+4) solution.

y = 4x+8

y = 4x+8

x -y = -1

y =x-2+3

-x =-x

y =x+1

-y = -1-x

-1 = -1

y= 1 +x

y= x + 1

Slope:1, y-intercept: 1

y =x+1

Slope:1, y-intercept: 1

y =x-2+3

y =x+1

y solution.=x+1

y =x-2+3

y =x+1

y-3x = 3 solution.

y =3(x+1)

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