Pair of Linear Equations in Two Variables — Practice

Question 1

By comparing ratios, state whether the lines 5x - 4y + 8 = 0 and 7x + 6y - 9 = 0 intersect at a point, are parallel, or are coincident.

Accepted Answer

They intersect at a point

Question 2

By comparing ratios, state whether the lines 9x + 3y + 12 = 0 and 18x + 6y + 24 = 0 intersect at a point, are parallel, or are coincident.

Accepted Answer

They are coincident

Question 3

By comparing ratios, state whether the lines 6x - 3y + 10 = 0 and 2x - y + 9 = 0 intersect at a point, are parallel, or are coincident.

Accepted Answer

They are parallel

Question 4

Check whether x + y = 5 and 2x + 2y = 10 are consistent or inconsistent, and say how many solutions the pair has.

Accepted Answer

Consistent and dependent, with infinitely many solutions

Question 5

Ten students of Class X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys, find how many of each took part.

Accepted Answer

7 girls and 3 boys

Question 6

5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and one pen.

Accepted Answer

A pencil costs Rs 3 and a pen Rs 5

Question 7

The area of a rectangle gets reduced by 80 square units if its length is reduced by 5 units and the breadth increased by 2 units. If the length is increased by 10 units and the breadth decreased by 5 units, the area increases by 50 square units. Find the length and breadth.

Accepted Answer

Length 40 units, breadth 30 units

Question 8

In a class, if three students sit on each bench, one student is left. If four students sit on each bench, one bench is left. Find the number of students and the number of benches.

Accepted Answer

16 students and 5 benches

Question 9

The ratio of the incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them saves Rs 2000 per month, find their monthly incomes.

Accepted Answer

Rs 18000 and Rs 14000

Question 10

The sum of a two-digit number and the number obtained by reversing its digits is 66. If the digits differ by 2, find the number, and say how many such numbers there are.

Accepted Answer

42 and 24, so there are two such numbers

Question 11

Taxi charges in Hyderabad have a fixed component covering the first 3 km and a per-kilometre charge beyond that. For the first 10 km the charge is Rs 166 and for 15 km it is Rs 256. Find the fixed charge and the rate per km, and the cost of a 25 km journey.

Accepted Answer

Fixed charge Rs 40, rate Rs 18 per km, and a 25 km journey costs Rs 436

Question 12

A fraction becomes 4/5 if 1 is added to both numerator and denominator, and becomes 1/2 if 5 is subtracted from both. What is the fraction?

Accepted Answer

7/9

Question 13

Places A and B are 100 km apart. A car starts from A and another from B at the same time at different speeds. Travelling in the same direction they meet in 5 hours; travelling towards each other they meet in 1 hour. Find the two speeds.

Accepted Answer

60 km/h and 40 km/h

Question 14

A chemist has one 50% solution and one 80% solution of hydrochloric acid. How much of each should be used to obtain 100 ml of a 68% solution?

Accepted Answer

40 ml of the 50% solution and 60 ml of the 80% solution

Question 15

Solve by reducing to a pair of linear equations: 5/(x - 1) + 1/(y - 2) = 2 and 6/(x - 1) - 3/(y - 2) = 1.

Accepted Answer

x = 4 and y = 5

Question 16

Solve by reducing to a pair of linear equations: 1/(3x + y) + 1/(3x - y) = 3/4 and 1/(2(3x + y)) - 1/(2(3x - y)) = -1/8.

Accepted Answer

x = 1 and y = 1

Question 17

2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone and by 1 man alone.

Accepted Answer

One woman alone takes 18 days and one man alone 36 days

Question 18

Solve the equations 2^x + 3^y = 17 and 2^(x + 2) - 3^(y + 1) = 5.

Accepted Answer

x = 3 and y = 2

Question 19

Animals in an experiment must each receive 20 g of protein and 6 g of fat. Mix A is 10% protein and 6% fat; Mix B is 20% protein and 2% fat. How many grams of each mix should be used?

Accepted Answer

80 g of Mix A and 60 g of Mix B

Question 20

Which of the following is NOT a linear equation? (a) 5 + 4x = y + 3   (b) x + 2y = y - x   (c) 3 - x = y squared + 4   (d) x + y = 0

Accepted Answer

(c) 3 - x = y squared + 4

Practice — Pair of Linear Equations in Two Variables

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