Linear Equations in Two Variables Maths - Linear Equations in Two Variables

Ajay is younger than Vijay by 5 years. Sum of their ages is 25 years. What is Ajay’s age?

‘When 5 is subtracted from length and breadth of the rectangle, the perimeter becomes 26’. What is the mathematical form of the statement ?

If 3x + 5y = 9 and 5x + 3y = 7, then what is the value of x + y ?

Solve the following equations : m+3=5

Which number should be subtracted from 8 to obtain 2?

There are instructions written near the arrows in the following diagram. From this information form suitable equations and write in the boxes indicated by arrows. Select any two equations from these boxes and find their solutions. Also verify the solutions. By taking one pair of equations at a time, how many pairs can be formed ? Discuss the solutions for these pairs.

On the glasses of following spectacles, write numbers such that
i. Their sum is 42 and difference is 16.

ii. Their sum is 37 and difference is 11.

iii. Their sum is 54 and difference is 20.

iv. Their sum is … and difference is … .

By equating coefficients of variables, solve the following equations : 4x+y = 34 ; x + 4y = 16

By equating coefficients of variables, solve the following equations : x – 2y = -10 ; 3x – 3y = -12

The population of a certain town was 50,000. In a year, male population was increased by 5% and female population was increased by 3%. Now the population became 52020. Then what was the number of males and females in the previous year?

Solve. 3x – 4 y= 16 ; 2x – 3y = 10

Solve the following equations
3x + y = 5........... (I)
2x + 3y = 1........(II)

Solve x + y = 14 and x - y = 2 .

The sum of a two digit number and the number obtained by interchanging its digits is 99. Find the number.

The distance between two places A and B on a road is 70 kilometres. A car starts from A and the other from B. If they travel in the same direction, they will meet in 7 hours. If they travel towards each other they will meet in 1 hour, then find their speeds.

If the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 9 square units. If length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.

The ratio of incomes of two persons is 9 : 7. The ratio of their expenses is 4 : 3. Every person saves ₹ 200, find the income of each.

The total cost of 8 books and 5 pens is ₹ 420 and the total cost of 5 books and 8 pens is ₹321. Find the cost of 1 book and 2 pens.