Intro to System of Linear Equations Graphically

Multiple Choice

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Multiple Choice

^{What is the solution?} 

• 1

• -2

• (1, 2)

• (1, -1)

Multiple Choice

What kind of lines are these?

• Parallel lines

• Line segments

• Perpendicular Lines

• Intersecting lines

System of Equations: Types of Solutions

A Graphical Approach

(One Solution)

Where ever the graphs of linear functions intersect we have a solution.

In this case we have one solution for the system y = -x + 7 and y = 2x + 1 at the point (2, 5).

A Graphical Approach

(No Solutions)

When lines never intersect, then there are no solutions to the system of equations.

Notice in the example that the lines have the same slope and different y-intercepts. (Recall: y=mx+b)

A Graphical Approach

(Infinitely Many Solutions)

Notice in the example that the equations look different at first, but after a little algebra, we see that they are the same line. There are infinitely many solutions.

Multiple Choice

How many solutions does this system of equations have?

• one solution

• no solution

• infinite solutions

• 2 solutions

Multiple Choice

How many solutions does this system of equations have?

• No solution

• Infinite solutions

• 1 solution

• 2 solutions

Multiple Choice

How many solutions will this system have?

• No Solution

• Infinitely Many Solutions

• No Clue

• One solution

Multiple Choice

• (1, 1)

• (1, -1)

• (1, - 2)

• (0, -1)

Fill in the Blanks

Type the solution to the system of equations as an ordered pair, (x,y).

Multiple Choice

Which figure has no solutions

• Figure 1

• Figure 2

• Figure 3

• Figure 4

Dropdown

Parallel lines have the same ​ ​

Select answer

.

Dropdown

Parallel lines have the ​

Select answer

y-intercepts.

How do we determine parallel lines?

• parallel lines have the SAME slope.

• parallel lines have DIFFERENT y-intercepts.

​No Solutions

How do we determine lines are Identical?

• parallel lines have the SAME slope.

• parallel lines have SAME y-intercepts.

​Infinite Solutions

Linear Systems can have the following types of solutions

Multiple Choice

$$y=7x+2\ \ and\ y=7x-1$$  

• perpendicular

• parallel

• neither

• Same line

Multiple Choice

$$y=4x-5\ \ and\ y=4x-5$$  

• perpendicular

• parallel

• neither

• Same Line

Multiple Choice

How Many Solutions

y = 12x + 4 and y = 12x +14

• None

• 1

• 2

• Infinite

Multiple Choice

How Many Solutions

$$y=-\frac{1}{2}x+1\ and\ \ y=\frac{1}{2}x-5$$

• None

• 1

• 2

• Infinite

Multiple Choice

How many solutions

y=5x + 7 and y=5x + 7

• None

• 1

• 2

• Infinite

Multiple Choice

How many solutions

y= -8x + 12 and y= -8x - 12

• None

• 1

• 2

• Infinite