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# 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.

**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,