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Linear Equations Quiz - CBSE Class 8 Mathematics

Free practice quiz: Linear Equations (CBSE Class 8 Mathematics). 17 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 8 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.

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Learn the key ideas Beta

Solving Equations in One Variable

  • A linear equation has variables only to the first power: no squares, no products of variables, no variables in denominators.
  • Do the same operation on both sides. Move variable terms to one side and number terms to the other.
  • If the variable cancels and a false statement remains, there is no solution. If a true statement remains, every value works.
Basic form (a not zero)
\[ax + b = k \Rightarrow x = \frac{k - b}{a},\ a \neq 0\]
Variable on both sides
\[ax + b = px + q \Rightarrow x = \frac{q - b}{a - p},\ a \neq p\]

Common mistake: Forgetting to change the sign when a term is moved across the equals sign, for example writing +b instead of -b.

Slope and Intercepts of Lines

  • In y = mx + c, m is the slope. It is the rise divided by the run and shows how steep the line is.
  • c is the y-intercept, where the line crosses the y-axis. The x-intercept is where the line crosses the x-axis (y is zero).
Slope-intercept form
\[y = mx + c\]
Make y the subject (b not zero)
\[ax + by = k \Rightarrow y = \frac{k - ax}{b},\ b \neq 0\]
x-intercept of ax + by = k (a not zero)
\[x = \frac{k}{a},\ a \neq 0\]
y-intercept of ax + by = k (b not zero)
\[y = \frac{k}{b},\ b \neq 0\]

Common mistake: Reading the slope from ax + by = k without first making y the subject. The slope is -a/b, not a.

Parallel and Perpendicular Lines

  • Parallel lines have the same slope but different y-intercepts, so they never meet.
  • Perpendicular lines meet at a right angle. Their slopes are negative reciprocals: flip one slope and change its sign.
Parallel: y = mx + c and y = nx + d
\[m = n,\ c \neq d\]

Common mistake: Thinking perpendicular lines have equal slopes, or forgetting to change the sign when taking the reciprocal.

Solving a Pair of Equations

  • Use substitution (make one variable the subject, then substitute) or elimination (add or subtract to remove one variable).
  • The solution is the point where the two lines meet. If both equations give y, set them equal to find x.
  • The determinant shows whether the lines meet at exactly one point or have the same slope.
Determinant for ax + by = k and px + qy = r
\[D = aq - bp\]
Exactly one solution: lines intersect at one point
\[D \neq 0\]
Same slope: parallel (no solution) or coincident (infinitely many solutions)
\[D = 0\]

Common mistake: Assuming D = 0 always means no solution. If the two equations describe the same line, there are infinitely many solutions.

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 value of x in the equation 2x + 3 = 7?

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    Answer: B. x = 2

    To solve for x, first subtract 3 from both sides of the equation to get 2x = 4. Then, divide both sides by 2, yielding x = 2.

  2. What is the slope of the line represented by the equation y = 2x + 1?

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    Answer: C. 2

    In the slope-intercept form (y = mx + b), 'm' represents the slope. Here, 'm' is 2.

  3. What is the x-intercept of the line given by the equation 3x + 2y = 6?

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    Answer: B. (2,0)

    To find the x-intercept, set y = 0 in the equation: 3x + 2(0) = 6, which simplifies to 3x = 6. Solving gives x = 2. Thus, the x-intercept is (2,0).

  4. If m1 and m2 are the slopes of two lines that are perpendicular, what is the relationship between them?

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    Answer: C. m1 * m2 = -1

    For two perpendicular lines, the product of their slopes is -1.

  5. How do you rearrange the equation 4x - 3y = 12 to find y in terms of x?

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    Answer: A. y = (4/3)x - 4

    Rearrange to isolate y: 3y = 4x - 12, then divide by 3 to get y = (4/3)x - 4.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. Which of the following equations represents a linear relationship?
  2. If 3x - 4 = 5, what is the value of x?
  3. How many solutions does the equation 0x = 5 have?
  4. What is the value of x in the equation 5x + 3 = 3x + 11?
  5. What does the term 'slope' represent in a linear equation?
  6. Which method can be used to solve the system of equations 2x + y = 10 and x - y = 2?
  7. In the equation y = mx + c, what does 'c' represent?
  8. What is the point of intersection of the lines y = 2x + 1 and y = -x + 4?
  9. Which method is most effective for solving a large system of equations?
  10. What must be true for the equations y = 2x + 1 and y = 2x - 3 to be parallel?
  11. What is the geometric significance of the determinant of a 2x2 matrix formed by the coefficients of a system of linear equations?
  12. If the equations y = mx + b and y = -1/mx + c represent two lines, what would they be classified as if m is non-zero?

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