6.1.1 Linear Systems & Graphing Methods 1 & 2

Hotspot

Which of the linear systems have no solution?

Match

Match the linear system of equations with the number of solutions each will have.

no solutions

infinitely many solutions

one solution

• no solutions

• infinitely many solutions

• one solution

Multiple Choice

The graph shows two lines of a linear system being graphed. How many solutions does the linear system have?

• You cannot tell based on the graph

• Infinitely many solutions

• one solution

• no solution

Hotspot

Which point shows the solution to the linear system?

Draw

Draw an example of a graph of a system of linear equations that has no solution.

Multiple Choice

What is the solution of the graphed system of linear equations shown?

• (-1, 2)

• (2, -1)

• (0, -4)

• (3, 0)

Reorder

Sort the following steps in order on how you would solve a system of linear equations.

• Plot the first y-intercept on the y-axis

• Use the first slope to plot another point and connect them to draw the first line.

• Plot the second y-intercept on the y-axis.

• Use the second slope to plot another point and connect them to draw the second line.

• Find the coordinates of the point of intersection to determine the solution of the system of equations

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Draw

What is the slope and y-intercept for both equations? Then graph the equations to find the solution to the system.

Draw

On the graph , solve the system of equations by graphing both linear equations and write the solution.

$$y=x+2$$

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

Multiple Choice

What is the solution to the system of equations shown in the graph?

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

$$y=x+1$$

• (0, 3)

• (3, 4)

• (4, 3)

• (-1, 0)

Multiple Choice

Which graph accurately represents the system of equations

y = x+2

y=2(x+1)+2

Math Response

What is the equation 4x + 2y = 10 in slope-intercept form?

Type answer here

Correct Answer: y=-2x+5

Deg^°

Rad

Draw

1.Write each equation in slope-intercept form if needed.

2.Then, solve the system of linear equations by graphing.

Multiple Select

Which statements accurately describe the graph?

Select all that apply

• No solution

• one solution

• different slopes

• Same slopes

Multiple Select

Which statements accurately describe the graph?

Select all that apply

• No solution

• infinitely many solutions

• different slopes

• Same slopes but different y-intercepts

• parallel lines

Multiple Select

Which statements accurately describe the graph?

Select all that apply

• No solution

• infinitely many solutions

• Same slope and same y-intercept

• Same slopes but different y-intercepts

• parallel lines

Multiple Choice

What is the solution to the linear system?

y = (x + 6) - 2

y = -x + 2

• (0, 2)

• (-4, 0)

• (1, 3)

• (-1, 3)