Systems of Equations in Two and Three Variables

What if you are solving a system and the variables cancel out and you end up with a statement such as 3=3, what can you conclude about the system?

• the solution is 3

• there are no solutions

• you can't conclude anything

• there are infinite solutions

What is the solution to the system?

• (5,-3,2)

• (-3,5,2)

• no solution

• infinite solutions

What would you solve for First?

• Solve for x

• Solve for y

• Solve for z

• (5,3,4)

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

What are systems of linear equations?

• a set of two or more linear equations in the same variables

• a polynomial with three terms

• set of two or more linear inequalities in the same variables

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

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

• Parallel lines

• the same line

• Intersecting lines

Solve the following system of equations by graphing:

• (4, -4)

• (-4, 4)

• no solutions

• (0, 0)

Solve the following system of equations using the elimination method:

• (-2, 1)

• no solutions

• (-2, 0)

• (-1, -3)