# Worksheet: Consistency and Dependency of Linear Systems

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.

**Q3: **

Your friend is thinking of two numbers. She tells you that the numbers add up to 104. Also, two times the first number plus two times the second number is 208. Is it possible to work out the numbers your friend chose?

- AYes, the system of equations is independent.
- BNo, the system of equations is inconsistent.
- CNo, there are infinitely many solutions.

**Q5: **

A food drive collected two different types of canned goods: green beans and kidney beans. Overall, they collected 350 cans whose total weight was 348 lb 12 oz. If you know that the green bean cans weigh 2 oz less than the kidney bean cans, is it possible to find how many of each can was donated?

- ANo, there are multiple solutions.
- BNo, the system is inconsistent.
- CYes, the system is independent.

**Q7: **

Admission into an amusement park for 4 children and 2 adults is $116.90. For 6 children and 3 adults, the total price is $175.35. Assuming the price for children and adults is different, what type of system of equations does the scenario create?

- Adependent system of equations
- Bindependent system of equations
- Cinconsistent system of equations

**Q8: **

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.

**Q9: **

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.

**Q10: **

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.

**Q13: **

Find the number of solutions to the system of equations

- AOne
- BNone
- CInfinitely many

**Q14: **

Find the number of solutions to the system of equations

- AInfinitely many
- BNone
- COne

**Q15: **

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

- Ayes,
- Byes,
- Cyes,
- Dno
- Eyes,

**Q24: **

How many solutions can a linear equation with variable have? Pick all possible answers.

- 0 solutions
- 1 solution
- more than 3 solutions
- 2 solutions

- Aa, b, c
- Ba only
- Cb, c
- Da, b
- Eb only