$CATEGORY: Maths - TicTacLearn/3. Pair of linear equations in two variables/3. Pair of linear equations in two variables--Introduction

//Multiple Choice

You have ₹50 to buy balloons and ice creams. Balloons cost ₹5 each, and ice creams cost ₹10 each. If you buy 2 balloons, how many ice creams can you buy? {
~ 3
~ 2
= 4
~ 1
}

A bus ticket costs ₹20, and a train ticket costs ₹50. You spend ₹220 on 6 tickets in total. How many bus tickets did you buy? {
~ 2
~ 3
= 4
~ 5
}

You bought 5 notebooks and 3 pens for ₹120. If a notebook costs ₹20, what is the cost of one pen? {
~ ₹10
~ ₹20
~ ₹15
= ₹7
}

A shop sells apples at ₹30 per kg and bananas at ₹20 per kg. If you buy 2 kg of apples and 3 kg of bananas for ₹120, how much does 1 kg of bananas cost? {
= ₹20
~ ₹25
~ ₹30
~ ₹15
}

You have ₹100 to buy pencils and erasers. Pencils cost ₹5 each, and erasers cost ₹10 each. If you buy 4 pencils, how many erasers can you buy? {
~ 6
~ 4
= 8
~ 5
}

A taxi charges ₹50 as a base fare and ₹10 per km. If your total fare is ₹150, how many kilometers did you travel? {
= 10 km
~ 12 km
~ 15 km
~ 20 km
}

You bought 7 chocolates and 5 candies for ₹85. If each chocolate costs ₹8, what is the cost of one candy? {
~ ₹5
~ ₹4
~ ₹3
= ₹6
}

A movie ticket costs ₹150, and a popcorn combo costs ₹100. If you spent ₹600 buying 4 items in total, how many movie tickets did you buy? {
~ 2
~ 3
~ 1
= 4
}

You have ₹200 to spend on pizzas and burgers. A pizza costs ₹80, and a burger costs ₹40. If you buy 1 pizza, how many burgers can you buy? {
~ 3
= 2
~ 4
~ 1
}

A car rental company charges ₹500 as a base fee and ₹15 per km. If your total bill is ₹950, how many kilometers did you travel? {
~ 30 km
~ 35 km
= 30 km
~ 45 km
}

//True or False

If the cost of 2 pencils and 3 erasers is ₹25, and the cost of 1 pencil is ₹5, then the cost of 1 eraser is ₹5. {T}

If a taxi charges ₹50 as a base fare and ₹10 per km, then traveling 10 km will cost ₹150. {T}

You have ₹100 to buy 2 kg of apples at ₹40 per kg and 1 kg of bananas at ₹20 per kg. You can afford this purchase. {T}

If a movie ticket costs ₹150 and a popcorn combo costs ₹100, then buying 2 movie tickets and 1 popcorn combo will cost ₹500. {F}

The cost of 3 pens and 2 notebooks is ₹60. If the cost of 1 pen is ₹10, then the cost of 1 notebook is ₹15. {T}

If a bus ticket costs ₹20 and a train ticket costs ₹50, spending ₹200 on 4 tickets means you bought 2 bus tickets and 2 train tickets. {T}

A shop sells apples at ₹30 per kg and bananas at ₹20 per kg. Buying 2 kg of apples and 3 kg of bananas will cost ₹150. {F}

You have ₹200 to buy pencils and erasers. If pencils cost ₹5 each and erasers cost ₹10 each, buying 10 pencils and 10 erasers will cost ₹200. {F}

If a car rental company charges ₹500 as a base fee and ₹15 per km, traveling 20 km will cost ₹800. {T}

If the cost of 5 chocolates is ₹50, then the cost of 3 chocolates is ₹30. {T}

//Numericals



//Fill in the blanks

A linear equation in two variables is of the form ax + by + c \= 0, where a, b, and c are __________. {
~ Variables
= Constants
~ Coefficients
}

The graph of a pair of linear equations in two variables can be __________, __________, or __________. {
= Parallel, intersecting, coincident
~ Straight, curved, circular
~ Horizontal, vertical, diagonal
}

If the pair of equations has no solution, the lines are __________. {
~ Intersecting
~ Coincident
= Parallel
}

If the pair of equations has infinitely many solutions, the two lines are __________. {
= Coincident
~ Parallel
~ Perpendicular
}

The general solution of a pair of linear equations in two variables is found using the __________ method. {
~ Graphical
~ Substitution
~ Elimination
= All of the above
}

The two linear equations 2x+3y\=5 and 4x+6y\=10 represent __________ lines. {
~ Parallel
= Coincident
~ Intersecting
}

If the ratio of the coefficients of x and y in two linear equations is equal but the ratio of the constant terms is not, then the lines are __________. {
~ Coincident
~ Intersecting
= Parallel
}

If two lines represented by linear equations intersect at a unique point, the system of equations has a __________ solution. {
= Unique
~ Infinite
~ No
}


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