Understanding Systems of Equations

The video tutorial explains the three types of solutions for systems of equations: consistent and independent (one solution), consistent and dependent (infinite solutions), and inconsistent (no solution). It provides examples and graphing instructions for each type, highlighting the characteristics of each system and how to identify them on a graph.

What is the term used for a system of equations with exactly one solution?

• Consistent and independent

• Consistent and dependent

• Dependent

• Inconsistent

When two lines overlap completely, what type of solution do they represent?

• No solution

• Infinite solutions

• One solution

• Inconsistent

What is the term for a system of equations that is consistent and dependent?

• Infinite solutions

• No solution

• Inconsistent

• One solution

What do we call a system of equations with parallel lines?

• Consistent and dependent

• Infinite solutions

• Consistent and independent

• Inconsistent

What happens when two lines in a system of equations are parallel?

• They form a circle

• They never intersect

• They overlap completely

• They intersect at one point

In the example with equations y = -x + 2 and y = x + 1, what is the solution point?

• (2, 2)

• (1, 1)

• (0.5, 1.5)

• (0, 0)

What color was used for the line y = x + 2 in the example?

• Blue

• Red

• Purple

• Green

In the example with equations y = x + 2 and 3x + 3y = -3, what is the nature of the solution?

• No solution

• Inconsistent

• One solution

• Infinite solutions

What is the color of the line 3x + 3y = -3 in the infinite solutions example?

• Red

• Blue

• Purple

• Black

In the example with infinite solutions, what is the equation of the line that overlaps with y = x - 1?

• y = x + 1

• 3x + 3y = -3

• y = x + 2

• y = -x + 2