PDF chapter test TRY NOW
Let us recall the concept of linear equations in two variables.
An equation in which two variables x and y is of the first degree is said to be a linear equation in two variables.
The general form of linear equation in two variables can be written as:
ax + by + c = 0
Here, atleast one of a, b is non-zero,
x and y are variables and
a, b and c are real numbers.
Example:
The mother's age is equal to the sum of the ages of her 4 children. After 17 years, twice the mother's age will be the sum of ages of her children. First, fnd the age of the mother.
Solution:
To find: The age of the mother.
Explanation: Let x denote the age of the mother and y represents the sum of the ages of her 4 children.
x = y ---- (1)
2(x + 17) = (y + 4 \times 17)
2x + 34 = y + 68
2x - y - 34 = 0 ---- (2)
Substitute equation (1) in (2).
2y - y - 34 = 0
y - 34 = 0
y = 34
Substitute the value of y in equation (1), we get:
x = 34
Therefore, the mother's age is 34 years.
2. 3 sandwiches and 2 glass of juice cost ₹700 and 5 sandwiches and 3 glass of juice cost ₹1100. What is the cost of a sandwich and a glass of juice?
Solution:
To find: The cost of a sandwich and a glass of juice.
Explanation: Let x denote the cost of a sandwich, and y represent the price of a glass of juice.
3x + 2y = 700 ---- (1)
5x + 3y = 1100 ---- (2)
Let us solve using the elimination method.
(1) \times 3 \Rightarrow 9x + 6y = 2100
(2) \times 2 \Rightarrow 10x + 6y = 2200
------------------------------------------------
- x = - 100
x = 100
Substitute the value of x in equation (1), we get:
3(100) + 2y = 700
300 + 2y = 700
2y = 400
y = 200
Therefore, the cost of a sandwich is ₹100 and the price of a glass of juice is ₹200.
Register for free to see more content