𝑦=5𝑥−4
𝑦=−2𝑥+3
𝑦=3𝑥+1
2𝑦=6𝑥+2
𝑦−5𝑥=2
𝑦−4𝑥+1=0
Complete steps a. through e. to determine which pair of equations form a system with one solution, no solution, or infinite solutions.
Solve each equation and make sure it is in 𝑦=𝑚𝑥+𝑏
y=mx+b
format.
Graph all six equations on the coordinate grid and label them.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1.
Circle the two equations that form a system with infinite solutions.
Put a square around the two equations that form a system with no solution.
Underline the two equations that form a system with one solution.
What do you notice about equations that are in each of these categories? Use complete sentences to answer the questions that follow.
Question 2: Infinite Solutions
Consider the two equations you circled, which form a system with infinite solutions. Graph them together on the following coordinate grid.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1.
What do you notice about these graphs? What does it mean for a system to have infinite solutions? What do the graphs of a system with infinite solutions look like? Explain what it means graphically for a system to have infinite solutions.
Plug a few points into the original equations and check to show that the system of equations has more than one solution. Explain your work.
Question 3: No Solution
Consider the two equations you put a square around, which form a system with no solution. Graph them together on the following coordinate grid.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1.
What do you notice about these equations? What does it mean for a system to have no solution? Explain what it means graphically for a system to have no solution.
Plug a few points into the original equations and check to show that the system of equations has no solution. Explain your work.
Question 4: One Solution
Consider the two equations you underlined, which form a system with one solution. Graph them together on the following coordinate grid.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1.
What do you notice about these equations? What does it mean for a system to have one solution? Explain what it means graphically for a system to have one solution.
Plug a few points into the original equations and check to show that the system of equations has one solution. Explain your work.
3 answers
I see a fairly clear set of instructions.
1 answer