Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Number of Solutions to a System of Linear Equations

Q1:

How many solutions are there to the simultaneous equations π‘₯ + 7 𝑦 = 2 0 and 2 π‘₯ + 1 4 𝑦 = 4 0 ?

  • Aa unique solution
  • Btwo solutions
  • Czero
  • Dan infinite number of solutions

Q2:

If the simultaneous equations 6 π‘₯ + 7 𝑦 = 2 and 1 8 π‘₯ + π‘˜ 𝑦 = 6 have an infinite number of solutions, what is the value of π‘˜ ?

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.

Q4:

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

  • Ayes,
  • Byes,
  • Cyes,
  • Dno
  • Eyes,

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?

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

Q6:

What is the value of π‘˜ for which the simultaneous equations π‘₯ + 2 𝑦 = 1 and 5 π‘₯ + π‘˜ 𝑦 = 5 do not have a unique solution?

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?

  • Aindependent system of equations
  • Binconsistent system of equations
  • Cdependent system of equations

Q8:

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

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

Q9:

Consider the three equations

  1. π‘₯ + 1 = 3 ,
  2. ( π‘₯ + 1 ) = 9  ,
  3. ( π‘₯ + 1 ) = 2 7  .

Which equations have the same solution set?

  • Anone
  • B(A), (B), and (C)
  • C(A) and (B) only
  • D(A) and (C) only
  • E(B) and (C) only

Q10:

The simultaneous equations represented by the straight lines 𝐿 1 and 𝐿 2 have an infinite number of solutions. Which of the following describes the relationship between the lines 𝐿 1 and 𝐿 2 ?

  • AThey are perpendicular.
  • BThey are parallel.
  • CThey intersect in one point.
  • 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 coincident.
  • BThey are perpendicular.
  • CThey are skew.
  • DThey are parallel.
  • EThey are neither parallel nor perpendicular.

Q12:

Suppose a system of equations has fewer equations than variables. Must such a system be consistent?

  • ANo
  • BYes

Q13:

If a system of equations has more equations than variables, can it have a solution?

  • Ayes
  • Bno

Q14:

Find the number of solutions to the system of equations

  • ANone
  • BInfinitely many
  • COne

Q15:

Find the number of solutions to the system of equations

  • AInfinitely many
  • BOne
  • CNone

Q16:

5 = 5 Γ— 5 4 3 1 and 5 Γ— 5 Γ— 5 Γ— 5 = ( 5 Γ— 5 Γ— 5 ) Γ— ( 5 ) .

This is an example of the product rule of exponents π‘Ž Γ— π‘Ž = π‘Ž π‘₯ 𝑦 π‘₯ + 𝑦 .

Which of the following is equivalent to 5 9 ?

  • A 5 Γ— 6 4 5
  • B 5 Γ— 5 3 3
  • C 5 Γ— 5 9 1
  • D 5 Γ— 5 3 6
  • E 5 + 5 6 3

Q17:

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

  • Ayes, π‘₯ = 1 , 𝑦 = 4
  • Byes, π‘₯ = 4 , 𝑦 = βˆ’ 1
  • Cyes, π‘₯ = 1 , 𝑦 = 1
  • Dno
  • Eyes, π‘₯ = 2 , 𝑦 = 3

Q18:

How many solutions are there to the simultaneous equations 𝑦 = π‘₯ and 𝑦 + π‘₯ = 1 6 ?

  • Azero
  • Btwo solutions
  • Can infinite number of solutions
  • Da unique solution

Q19:

How many solutions are there to the simultaneous equations 𝑦 = 8 and 𝑦 βˆ’ π‘₯ = 1 2 ?

  • Azero
  • Btwo solutions
  • Can infinite number of solutions
  • Da unique solution

Q20:

How many solutions are there to the simultaneous equations 𝑦 = 2 and 𝑦 βˆ’ π‘₯ = 1 9 ?

  • Azero
  • Btwo solutions
  • Can infinite number of solutions
  • Da unique solution

Q21:

How many solutions are there to the simultaneous equations 𝑦 = 7 and 𝑦 βˆ’ π‘₯ = 1 7 ?

  • Azero
  • Btwo solutions
  • Can infinite number of solutions
  • Da unique solution

Q22:

How many solutions are there to the simultaneous equations π‘₯ + 9 𝑦 = 1 1 and 6 π‘₯ + 5 4 𝑦 = 2 1 ?

  • Aa unique solution
  • Btwo solutions
  • Can infinite number of solutions
  • Dzero

Q23:

How many solutions are there to the simultaneous equations π‘₯ + 5 𝑦 = 2 5 and 8 π‘₯ + 4 0 𝑦 = 2 0 0 ?

  • Aa unique solution
  • Btwo solutions
  • Czero
  • Dan infinite number of solutions

Q24:

How many solutions are there to the simultaneous equations π‘₯ + 𝑦 = 4 and π‘₯ βˆ’ 𝑦 = 6 ?

  • Azero
  • Btwo solutions
  • Can infinite number of solutions
  • Da unique solution

Q25:

How many solutions are there to the simultaneous equations π‘₯ + 6 𝑦 = 1 6 and 4 π‘₯ + 2 4 𝑦 = 2 3 ?

  • Aa unique solution
  • Btwo solutions
  • Can infinite number of solutions
  • Dzero