System of Equations (Two Variables)

If 𝐴, 𝐵, and 𝐶 are real numbers and if 𝐴 and 𝐵 are both not equal to 0 then

𝐴𝑥 + 𝐵𝑦 = 𝐶 is called a __________.

• linear equation in one variable

• linear equation in two variables

• system of linear equations

• system of linear inequalities

How many solutions are there in the system of equations?

• No Solution

• Infinitely Many Solutions

• One Solution

• Two Solutions

What is the number of solutions to the system of equations? (Notice there are two lines graphed one on top of the other.)

• No Solution

• Infinitely Many Solutions

• One Solution

• Two Solutions

What is the solution to this system of equations? Choose the correct answer from the drop-down menu to complete the statement. The solution to the system of equations ​ (a)   .

• is located at (6.5, -0.5)

• does not exist

• is infinitely many

• is located at (-0.5, 6.5)

What is the solution to this system of equations? Choose the correct answer from the drop-down menu to complete the statement. The solution to the system of equations ​ (a)   .

• is located at (6.5, -0.5)

• does not exist

• is infinitely many

• is located at (-0.5, 6.5)

• (-7,7)

• (-7,-7)

• No Solution

• Infinite Solutions

• (7,-7)

What is the solution to this system of equations?

• is located at (6.5, -0.5)

• does not exist

• is infinitely many

• is located at (-0.5, 6.5)

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

• t: # of tacos
  m: # of glasses of milk

• t: Cost of each taco
  m: Cost of each glass of milk

• t: total cost
  m: # of food items

• t: Cost of each glass of milk
  m: Cost of each taco

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

What is the x-value of the solution to this system of equations?

Mathematical Equivalence

ON