4.6 Solve Simultaneous Linear Equations

Graphing

WARM UP:

Graph the Equation:     

$$y\ =\ -\frac{3}{2}x\ +\ 1$$

Today's lesson will involve finding solutions to simultaneous linear equations:

​Solution: ( 1 , 4 )

​For Example:

The lines y = 4x AND y = x + 3
are graphed to the right. The point of
intersection is the solution to the equations.

How are simultaneous linear equations seen in real life?
Part 1 Part 2

Match

Match the following graphs with their solution type:

One Solution

Infinite Solutions

No Solution

• One Solution

• Infinite Solutions

• No Solution

Multiple Choice

y = 5x + 1

What are the slope and y-intercept of this equation?

• m = 5 and b = x

• m = 1 and b = 5

• m = 5 and b = 1

• m = x and b = 1

y = -2x - 3


y = 2x + 5

​Identify and verify the x and y values that simultaneously satisfy the following equations:

Graphing

​Identify and verify the x and y values that simultaneously satisfy the following equations:

$$y\ =\ \frac{1}{3}x\ +\ 2$$

$$y\ =\ 3x\ -\ 6\$$

(This one is already graphed)

Multiple Choice

What is the solution to the system of equations?

• (5, 2)

• (2, 5)

• (-5, 2)

• (-2, -5)

Multiple Choice

What is the solution to the system of equations?

• (-5, -2)

• (2, -5)

• (2, 5)

• (-5, 2)

Multiple Choice

What is the solution to the following system of equations?

• (0,3)

• (-3, 1)

• (1, 3)

• Infinitely Many Solutions

• No Solution

Multiple Choice

How many solutions are there for the graph of y=2x+1 and y=2x-3

• One Solution

• Infinite Solutions

• No Solutions

• Two Solutions

Multiple Choice

What can you conclude about the slopes and y-intercepts of the equations when a system of equations has no solution?

• Slopes and the y-intercepts are different

• Slopes are equal and the y-intercepts are different

• Slopes and the y-intercepts are equal

• information is incomplete to comment

Multiple Choice

What can you conclude about the slopes and y-intercepts of the equations when a system of equations has infinitely many solutions?

• Slopes are different and the y-intercepts are equal.

• Slopes and the y-intercepts are different.

• Both slopes and the y-intercepts are equal.

• Slopes are equal and the y-intercepts are different.

Multiple Choice

Frank and Erica are selling ribbons to raise money for the football team. The graph shows the linear relationship between the number of ribbons each of them has left to sell and the number of days that they have been selling ribbons.

On which day does it appear that Frank and Erica will have the same number of ribbons left to sell?

• 33

• 18

• 48

• 15

Multiple Choice

What is the point of intersection of these two lines? Where are they simultaneous?

• (0, 4)

• (3, 3)

• (-4, 0)

• (-3, 3)

Fill in the Blanks

Look at the graph on your paper.

Graph the two linear equations and write the coordinates (x,y) that satisfy the simultaneous linear equations.

Be sure to include parenthesis.

Fill in the Blanks

Look at the graph on your paper.

Graph the two linear equations and write the coordinates (x,y) that satisfy the simultaneous linear equations.

Be sure to include parenthesis.