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

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?

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

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

- What are the possible number of solutions for a system of linear equations?

- 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

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