Consistent and Inconsistent Equations

Consider the system of equations 3x + 4y = 0 -3x +-4y = 2 Adding the two equations side-by-side and simplifying yields 0 = 2. Which of the following can be concluded about the system of equations?

• It has a unique solution (2, 0).

• It has exactly two solutions (2, 0) and (0, 2).

• It has infinitely many solutions.

• It has no solution.

Answer explanation

Since both sides of the equation do not equal each other, this is how you can tell that a problem has no solution.

a situation where there is one or infinitely many solutions that satisfies all of the equations in the system; this happens when lines are intersecting

• no solution

• consistent system

• inconsistent system

• parallel lines

if a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0 has infinitely many solutions then,

• 
• 
• 
• 

• No solution

• Infinite solutions

How may solutions does this graph have?

• None

• 1

• 3

• Infinitely many

WITHOUT GRAPHING
what can you say about these lines

• Consistent and Dependent

• Consistent and Independent

• Neither

• Inconsistent

What is the solution to this system of equations?

• (1,0)

• (-3, -1)

• (-1,-3)

• (1,3)

What is the solution to this system of equations?

• (1,4)

• (4,1)

• (3,5)

• (-1, 4)

WITHOUT GRAPHING
what can you say about these lines

• Consistent and Dependent

• Consistent and Independent

• Inconsistent and Dependent

• Inconsistent and Independent

WITHOUT GRAPHING
what can you say about these lines

• Consistent and Dependent

• Consistent and Independent

• Inconsistent and Dependent

• Inconsistent and Independent