Two unknowns, one equation
What makes an equation have two variables?
Notebooks at ₹4 and pens at ₹3 totalling ₹24 gives $4x + 3y = 24$.
📚 Chapter Learning Kit
Two Variables, One Line · Class 9 Mathematics
English 3 topics 174 leveled MCQs 60 flashcards 4 games Free
Shared by a Veda teacher · Generated with Veda AI · Oct 2026
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✏️ Example
The whole idea, one bite at a time
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. Here's a taste from this kit; the app has the full deck.
Everything moved to one side
What is the standard form?
The standard form is $ax + by + c = 0$, with $a$ and $b$ not both zero.
First powers only, never multiplied
What does linear rule out?
$x^2 + y = 5$ is not linear, because $x$ is squared.
Rise over run
How do you measure steepness?
Walk from one point of the line to another and count both steps.
Change in $y$ over change in $x$
What is the formula from two points?
For $(x_1, y_1)$ and $(x_2, y_2)$, the slope is $m = (y_2 - y_1)/(x_2 - x_1)$.
It is 3
Slope through $P(1,2)$ and $Q(4,11)$?
The rise is $11 - 2 = 9$ and the run is $4 - 1 = 3$.
📖 Smart notes
What you'll study, topic by topic
1
Linear equations in two variables and their graphs
With two unknowns a solution is a PAIR, not a number, and there are infinitely many of them. Written as $ax + by + c = 0$, every such equation has a straight line for its graph, and that line is exactly the set of its so…
~40 min · full explanation, examples & memory tricks in the app
2
Slope and the slope-intercept form
Slope measures steepness as rise over run, and any two points of a line give the same value — which is why a line has one slope. Its sign says which way the line leans, 0 means horizontal, and a vertical line has no slop…
~40 min · full explanation, examples & memory tricks in the app
3
Pairs of linear equations and their solutions
A solution of a PAIR must satisfy both equations, so it is a point on both lines. Substitution and elimination find it algebraically, and because two lines can only cross once, run parallel, or coincide, a pair has exact…
~45 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
174 questions laddered from warm-up to topper-level, each with an explanation. A taste:
A linear equation in two variables is one in which
Beginner
A the two variables are multiplied together
B one variable is squared and the other is not
C there is exactly one solution for each variable, so naming one value settles the other
D each variable appears to the first power and they are not multiplied together
Show answer & explanation
each variable appears to the first power and they are not multiplied together
Linear means first powers only, with no products.
The standard form of a linear equation in two variables is
Beginner
A $ax + by + c = 0$, with $a$ and $b$ not both zero
B $ax + by = c$, with $c$ nonzero, so that the equation always has a constant term
C $ax^2 + by + c = 0$
D $axy + c = 0$
Show answer & explanation
$ax + by + c = 0$, with $a$ and $b$ not both zero
Both variables to the first power, everything on one side.
Written in standard form, $4x + 3y = 24$ becomes
Beginner
A $4x + 3y + 24 = 0$
B $4x + 3y - 24 = 0$
C $4x - 3y - 24 = 0$
D $24 - 4x - 3y = 24$
Show answer & explanation
$4x + 3y - 24 = 0$
Move the constant to the left.
In $4x + 3y - 24 = 0$, the value of $c$ is
Beginner
A $24$
B $3$
C $-24$
D $4$
Show answer & explanation
$-24$
$c$ is the constant term as it stands on the left.
🃏 Flashcards
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60 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
🎮 Learning games
Play your way through this kit
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
Word Match
True False
Fill Blank
Word Scramble
Playable in the app
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The full Veda Bites deck, complete notes, spaced-repetition flashcards, leveled MCQs, tests and games for this kit — plus Daily Facts and the Arena, every day.