Systems of Equations with Inspection

Kai and Nora are trying to solve a system of two linear equations but they find that there are no solutions. What can they conclude about the graphs of the two equations they are trying to solve? (8.EEI.C.8c)

• The lines representing the equations have the same slope and the same y-intercept.

• The lines representing the equations have the same slope and different y-intercepts.

• The lines representing the equations have different slopes and the same y-intercept.

• The lines representing the equations have different slopes and different y-intercepts.

Tags

8.EEI.C.8.c

The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. Write the equations needed to solve the problem: (8.EEI.C.8d)

Tags

8.EEI.C.8d

8.EEI.C.8.d

Anika, Aiden, and Elijah are trying to determine the number of solutions for a system of equations they encountered while studying. The equations are as follows: y=\frac{2}{3}x-6 y=\frac{2}{3}x+3 How many solutions does this system have, and why?

• There are no solutions because the slopes and y-intercepts are the same.

• There are infinitely many solutions because the slopes and y-intercepts are the same.

• There are no solutions because the slopes are the same and the y-intercepts are different.

• There are infinitely many solutions because the slopes are the same and the y-intercepts are different.

Tags

8.EEI.C.8c

Tags

8.EEI.C.8b

• 10

• 4

• 5

• 6

• 7

• 8

• 9

• 3

• 2

Jerry buys gray modeling clay and pink modeling clay. Gray modeling clay cost $4 per pound. Pink modeling clay costs $5 per pound. Jerry orders a total of 14 pounds of modeling clay for $60. To represent this situation, Jerry writes the system of equations shown (8.EEI.C.8b). Graph the linear equations on page 4 of the paper test.

Tags

8.EEI.C.8b

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

What is the Solution to this system?

• (2,-2)

• (-2,2)

• All Real Numbers

• No Solution