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

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# Can you look at a system of linear equations and tell how many solutions it has? - PowerPoint PPT Presentation

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 will learn to predict how many solutions a system of linear equations has by inspection.

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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 will learn to predict how many solutions a system of linear equations has by inspection.

Slope Intercept Form of an Equation

y = mx + b

slope

y-intercept

Graphing a linear equation

y = 2x + 1

slope

y-intercept

Assuming that all equations have one solution because those are the types of equations that are solved the most.

One None Infinitely Many

y = x - 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.

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.

Slope: 1, y-intercept: 1

y = x + 1

Slope: , y-intercept: 1

y = x + 1

Determine the number of solutions that the system has.

Slope: -5, y-intercept: 1

y = -5x + 1

Slope: -5, y-intercept: -2

y = -5x-2

In this lesson you learned to predict how many solutions a system of linear equations has by inspection.

Does the system of linear equations y=2x and y=2x+1 have infinitely many solutions? Explain your answer.

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