# Lesson Worksheet: Consistency and Dependency of Linear Systems Mathematics • 8th Grade

In this worksheet, we will practice determining the number of solutions for a system of linear equations and whether each system is consistent, inconsistent, or dependent.

Q1:

How many solutions are there to the simultaneous equations and ?

• Atwo solutions
• Ban infinite number of solutions
• Czero
• Da unique solution

Q2:

If the simultaneous equations and have an infinite number of solutions, what is the value of ?

Q3:

Is there a solution to the system of equations If yes, what is it?

• AYes,
• BNo
• CYes,
• DYes,
• EYes,

Q4:

What is the value of for which the simultaneous equations and do not have a unique solution?

Q5:

What is true, in two dimensions, for two linear equations that simultaneously have infinitely many solutions?

• ABoth equations represent parallel lines.
• BBoth equations represent perpendicular lines.
• CBoth equations represent horizontal lines.
• DBoth equations represent the same line.
• EBoth equations represent intersecting lines.

Q6:

The simultaneous equations represented by the straight lines and have an infinite number of solutions. Which of the following describes the relationship between the lines and ?

• AThey are coincident.
• BThey are perpendicular.
• CThey intersect in one point.
• DThey are parallel.

Q7:

What property, in two dimensions, is true for two lines represented by two linear equations that do NOT simultaneously have a solution?

• AThey are perpendicular.
• BThey are skew.
• CThey are neither parallel nor perpendicular.
• DThey are parallel.
• EThey are coincident.

Q8:

Find the number of solutions to the system of equations

• AOne
• BNone
• CInfinitely many

Q9:

Find the number of solutions to the system of equations

• AInfinitely many
• BNone
• COne

Q10:

Is there a solution to the simultaneous equations If yes, what is it?

• AYes,
• BYes,
• CYes,
• DNo
• EYes,

This lesson includes 4 additional questions and 36 additional question variations for subscribers.

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