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Linear Equations Quiz - CBSE Class 9 Mathematics

Free practice quiz: Linear Equations (CBSE Class 9 Mathematics). 17 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 9 Mathematics practice quiz has 17 multiple-choice questions on Linear Equations, and 17 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Start quiz: 17 questions, free

Learn the key ideas first ↓

Learn the key ideas Beta

Balance Both Sides

  • An equation is like a balance: both sides are equal.
  • Whatever you do to one side, do the same to the other side.
  • Undo addition by subtracting and undo multiplication by dividing, until the variable is alone.
Solving ax + b = c
\[ax + b = c \Rightarrow x = \frac{c - b}{a},\ a \neq 0\]
Same operation on both sides
\[p = q \Rightarrow p + k = q + k\]

Common mistake: Moving a term across the equals sign without changing its sign, for example keeping +b as +b instead of -b.

Removing Brackets First

  • If the variable is inside brackets, multiply the outside number into every term inside.
  • Then solve the simpler equation by balancing.
Distributive law
\[a(x + b) = ax + ab\]
With subtraction inside
\[a(x - b) = ax - ab\]

Common mistake: Multiplying only the first term inside the bracket, writing a(x + b) as ax + b.

Variable on Both Sides

  • Collect all variable terms on one side and all numbers on the other side.
  • Then combine like terms and divide by the coefficient of the variable.
Collecting terms
\[ax + b = cx + d \Rightarrow (a - c)x = d - b\]
Final answer
\[x = \frac{d - b}{a - c},\ a \neq c\]

Common mistake: Adding cx to both sides instead of subtracting it, so the variable terms do not cancel.

Solving Two Equations Together

  • Two equations in x and y can share one common solution (x, y).
  • Add or subtract the equations to remove one variable, then solve for the other.
  • Put that value back into either equation to find the second variable.
Add to remove y
\[(x + y) + (x - y) = p + q\]
Subtract to remove x
\[(x + y) - (x - y) = p - q\]

Common mistake: Finding only x and forgetting to substitute it back to find y.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is the solution to the equation 2x + 3 = 7?

    Show answer

    Answer: B. x = 2

    To solve 2x + 3 = 7, subtract 3 from both sides to get 2x = 4. Then divide by 2 to find x = 2.

  2. What is the value of y if 2y + 6 = 10?

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    Answer: B. y = 2

    Subtract 6 from both sides to get 2y = 4. Divide by 2 to find y = 2.

  3. For the equation 6x - 2 = 10, what is x?

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    Answer: A. x = 2

    Add 2 to both sides to get 6x = 12. Then divide by 6 to find x = 2.

  4. For which x is 3x + 4 = 19?

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    Answer: B. x = 5

    Subtract 4 from both sides to get 3x = 15. Divide by 3 to find x = 5.

  5. What is y if 5(y - 2) = 15?

    Show answer

    Answer: C. y = 5

    Divide both sides by 5 to get y - 2 = 3. Add 2 to find y = 5.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. Solve for y: 3y - 5 = 1.
  2. If x - 4 = 0, what is the value of x?
  3. Solve 5x - 9 = 11 for x.
  4. What is the solution to 2z + 8 = 12?
  5. Solve 4y + 10 = 18 for y.
  6. What is x if 7x + 5 = 26?
  7. Find the value of y: 8y - 16 = 48.
  8. Solve for y: 9 - 3y = 0.
  9. Find x if 2(x + 3) = 14.
  10. Solve 2x + 3 = x + 9.
  11. For what value of x is 4x + 8 = 2x + 14?
  12. (Complexity: 10) Solve for x and y in the equations x + y = 10 and x - y = 2.

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