Solving pairs of linear equations in two variables

Diego and Alex are running two different lemonade stands. They are trying to solve a system of equations representing the sales of lemonade at their respective stands. If the graphs of these equations do not intersect, what does it mean?

• The system of equations has infinitely many solutions, meaning both lemonade stands have the same sales.

• The system of equations has one solution, meaning there is a point where both lemonade stands have the same sales.

• The system of equations has no solution, meaning there is no point where both lemonade stands have the same sales.

• The solution to the system of equations is a complex number, meaning the sales of the lemonade stands cannot be compared directly.

Solve by Substitution.

y = 3x -4

y = 3x + 12

When solving a system algebraically, which expression indicates there is no solution?

Systems that have no solution when graphed

• Independent System

• Dependent System

• Inconsistent Systems

• Consistent Systems

• Solution Region

-5x + 5y = -5

x - 5y = -7

• (3, 2)

• (-1, 3)

• Infinite solutions

• No solutions

What is a no solution in a system of equations?

• The set of values that makes all of the equations in the system true

• A system of equations that has no set of values which will satisfy both equations

• A system of equations that has one intersection

• A system of equations in which both equations are exactly the same

Parallel lines have

• One solution

• No solution

• Infinitely many solutions

What is the solution of the following system of equations? Use graphing

y=-3x+4

y+3=-4

Which of the following is the solution for this system of linear equations?

• No Solution

• ( -3, 4 )

• ( 1, -2 )

• ( 2, 1 )

Solve:
x - 4y = -3
-3x - 3y = 24

• (-1, 0)
• (-7, 4)
• (-7, -1)
• No Solutions