# Worksheet: Number of Solutions to a System of Linear Equations

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

**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 lbβ12 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?

- AYes, the system is independent.
- BNo, the system is inconsistent.
- CNo, there are multiple solutions.

**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
- Binconsistent system of equations
- Cindependent system of equations

**Q8: **

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

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

**Q9: **

Consider the three equations

- ,
- ,
- .

Which equations have the same solution set?

- A(A) and (C) only
- Bnone
- C(A), (B), and (C)
- D(B) and (C) only
- E(A) and (B) only

**Q10: **

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

**Q11: **

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

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

**Q14: **

Find the number of solutions to the system of equations

- AInfinitely many
- BNone
- COne

**Q15: **

Find the number of solutions to the system of equations

- AInfinitely many
- BNone
- COne

**Q16: **

and .

This is an example of the product rule of exponents .

Which of the following is equivalent to ?

- A
- B
- C
- D
- E

**Q17: **

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

- Ayes,
- Bno
- Cyes,
- Dyes,
- Eyes,