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:

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What is a System of Equations?

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What is a system of equations

What is a System of Equations?

  • Use the iPads to find information about:

  • Uses

  • Ways to solve

  • Real-world applications

  • Types

  • Vocabulary


What is a system of equations

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?


What is a system of equations

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


What is a system of equations

Slope Intercept Form of an Equation

y = mx + b

slope

y-intercept


What is a system of equations

Graphing a linear equation

y = 2x + 1

slope

y-intercept


What is a system of equations

y = 2x + 1


What is a system of equations

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


What is a system of equations

There are three types of solutions for systems of linear equations

One None Infinitely Many


What is a system of equations

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


What is a system of equations

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


What is a system of equations

Determine the number of solutions that the system has.

Slope: 1, y-intercept: 1

y = x + 1

Slope: , y-intercept: 1

y = x + 1


What is a system of equations

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


What is a system of equations

How many solutions does the system of linear equations have?

y= -2x+1

y= -2x-2


What is a system of equations

How many solutions does the system of linear equations have?

y= -3x+1

y= -2x-7


What is a system of equations

How many solutions does the system of linear equations have?

y= -3(x+1)

y= -3x-3


What is a system of equations

  • 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=


What is a system of equations

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


What is a system of equations

What happens if we graph a system of equations and the lines intersect?

y = x-1

y = 2x-2


What is a system of equations

Not having the equation in slope- intercept form

y = 2 -x

3x + 2y = 4

y = -x + 2

-3x = -3x

2y = 4 -3x

Slope: -, y-intercept: 2

2 = 2


What is a system of equations

Graph the system of linear equations. Determine their solution.

y = x-1

y -2x = 2

+2x = +2x

y = 2 + 2x

y = 2x + 2


What is a system of equations

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


What is a system of equations

y = x-1

0 = 1-1

0 = 0

(1,0)

y = 2x-2

0 = 2*1-2

0 = 0


What is a system of equations

Graph the system of linear equations. Determine their solution.

y = x+3

-4x + y = 0

+4x = +4x

y = 4x


What is a system of equations

Graph the system of linear equations. Determine their solution.

Slope: 4, y-intercept: 0

y = 4x

Slope: 1, y-intercept: 3

y = x+3


What is a system of equations

y = 4x

4 = 4*1

(1,4)

4 = 4

y = x+3

4 = 1+3

4 = 4


What is a system of equations

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


What is a system of equations

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


What is a system of equations

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)


What is a system of equations

What happens if we graph a system of equations and the lines are parallel?

y = x

y = x- 1


What is a system of equations

Graph the system of linear equations. Determine their solution.

y - 4 = 2x

y = 2x

+ 4 = + 4

y = 2x + 4


What is a system of equations

Graph the system of linear equations. Determine their solution.

Slope: 2, y-intercept: 0

y = 2x

Slope: 2, y-intercept: 4

y = 2x+4


What is a system of equations

y = 2x

y = 2x+4


What is a system of equations

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


What is a system of equations

Graph the system of linear equations. Determine their solution.

Slope: , y-intercept: 0

y = x

Slope: , y-intercept: -1

y = x- 1


What is a system of equations

y = x

y = x- 1


What is a system of equations

y = x

y = x- 1


What is a system of equations

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


What is a system of equations

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


What is a system of equations

What happens if we graph a system of equations and the lines are the same?

y = 2(2x+4)

y = 4x+8


What is a system of equations

Graph the system of linear equations. Determine their solution.

y = 2(2x+4)

y – 4x = 8

y = 4x+8

+4x = +4x

y = 4x + 8


What is a system of equations

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


What is a system of equations

y = 2(2x+4)

y = 4x+8

y = 4x+8


What is a system of equations

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


What is a system of equations

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


What is a system of equations

y =x+1

y =x-2+3

y =x+1


What is a system of equations

y-3x = 3

y =3(x+1)


What is a system of equations

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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