Two Variables, One Line: CBSE Class 9 Mathematics practice questions

Practise 50 questions on Two Variables, One Line, free, with an explanation for each answer.

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Sample questions

Radha buys $x$ kg of mangoes at ₹60 per kg and $y$ kg of bananas at ₹50 per kg. She pays ₹280 in all. Which equation shows her purchase?

1. $60x + 50y = 280$
2. $50x + 60y = 280$
3. $x + y = 280$
4. $110(x + y) = 280$

Show the answer

A. $60x + 50y = 280$

The mangoes cost $60 \times x = 60x$ rupees and the bananas cost $50y$ rupees, so the total cost gives $60x + 50y = 280$. Writing $50x + 60y$ swaps the prices between the fruits. $x + y = 280$ forgets the prices and adds kilograms to rupees, and $110(x+y)$ wrongly treats both fruits as costing the sum of the two prices.

The point $(2,\ -1)$ lies on both lines $2mx + 3y = 7$ and $4x + ny = -10$. Find $m$ and $n$.

1. $m = \dfrac{5}{2},\ n = -18$
2. $m = \dfrac{5}{2},\ n = 18$
3. $m = 1,\ n = 18$
4. $m = \dfrac{7}{4},\ n = 18$

Show the answer

B. $m = \dfrac{5}{2},\ n = 18$

First equation: $2m(2) + 3(-1) = 7 \Rightarrow 4m - 3 = 7 \Rightarrow m = \dfrac{5}{2}$. Second: $4(2) + n(-1) = -10 \Rightarrow 8 - n = -10 \Rightarrow n = 18$. Traps: forgetting the $-3$ gives $m = \dfrac{7}{4}$, treating $3(-1)$ as $+3$ gives $m = 1$, and writing $8 + n = -10$ gives $n = -18$.

The incomes of two people are in the ratio $9 : 7$. Their expenses are in the ratio $4 : 3$. Each of them saves ₹3,000 a month. What is the monthly income of the first person?

1. ₹27,000
2. ₹3,000
3. ₹21,000
4. ₹24,000

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A. ₹27,000

Multiply by 3 and 4: $27x - 12y = 9000$ and $28x - 12y = 12000$. Subtracting the first from the second gives $x = 3000$, then $9(3000) - 4y = 3000$ gives $y = 6000$. The first income is $9x = ₹27{,}000$. ₹3,000 is just $x$, ₹21,000 is the second income, and ₹24,000 is the first person's spending $4y$.

Topics covered

• Forming a linear equation
• Standard form
• Linear equations in two variables
• Solution of an equation
• Finding unknown constants
• Solutions of an equation
• Intercepts on a graph
• Points and the line
• True or false about linear equations
• Lines through the origin
• Slope from two points
• Slope of a ramp
• Rise and run
• Slope-intercept form
• Graph of a line
• Types of slope
• Vertical and horizontal lines
• Parallel lines
• Comparing steepness
• Forming equations
• Pair of equations from a situation
• Solving a puzzle with two equations
• Substitution method
• Angles of a triangle
• Elimination method
• Elimination step by step
• Consistency of a pair
• Unique solution condition
• Coincident lines
• Number of solutions
• Graphs of pairs of equations
• Fraction problem
• Age problem
• Notes problem
• A Pinch of History
• Graphical solution
• Reading an intersection
• Identifying a line
• Two plans compared
• Choosing a plan
• Temperature conversion
• Meeting point of two paths
• Cyclic quadrilateral
• Graphical method
• Ordering slopes
• y-intercepts
• Solutions on a fruit bill
• Substitution step by step

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More CBSE Class 9 Mathematics chapters

• Orienting Yourself: The Use of Coordinates
• Introduction to Linear Polynomials
• The World of Numbers
• Exploring Algebraic Identities
• I’m Up and Down, and Round and Round
• Measuring Space: Perimeter and Area
• The Mathematics of Maybe: Introduction to Probability
• Predicting What Comes Next: Exploring Sequences and Progressions
• Propositions and Their Converses
• How Quantities Combine: Understanding Data
• The World of Algorithms
• Quadrilaterals
• Math of Space: Surface Area and Volume