Solutions: Exercise 4.1
1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
Let the cost of the notebook be ₹ x.
Let the cost of the pen be ₹ y.
According to the statement, “The cost of a notebook is twice the cost of a pen.”
This translates to the equation: x = 2y
To express this in the standard form ax + by + c = 0, we rearrange the terms:
2. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b, and c in each case:
2x + 3y = 9.35...Rearranging to standard form: 2x + 3y - 9.35... = 0
Comparing this with ax + by + c = 0, we get:
a = 2, b = 3, c = -9.35…
x - y/5 - 10 = 0The equation is already in standard form. We can write it as: 1x + (-1/5)y + (-10) = 0
Comparing this with ax + by + c = 0, we get:
a = 1, b = -1/5, c = -10
-2x + 3y = 6Rearranging to standard form: -2x + 3y - 6 = 0
Comparing this with ax + by + c = 0, we get:
a = -2, b = 3, c = -6
x = 3yRearranging to standard form: x - 3y = 0, which can be written as 1x - 3y + 0 = 0.
Comparing this with ax + by + c = 0, we get:
a = 1, b = -3, c = 0
2x = -5yRearranging to standard form: 2x + 5y = 0, which can be written as 2x + 5y + 0 = 0.
Comparing this with ax + by + c = 0, we get:
a = 2, b = 5, c = 0
3x + 2 = 0The term with y is missing, so its coefficient is 0. The equation is 3x + 0y + 2 = 0.
Comparing this with ax + by + c = 0, we get:
a = 3, b = 0, c = 2
y - 2 = 0The term with x is missing, so its coefficient is 0. The equation is 0x + 1y - 2 = 0.
Comparing this with ax + by + c = 0, we get:
a = 0, b = 1, c = -2
5 = 2xRearranging to standard form: -2x + 5 = 0 or 2x - 5 = 0. We will use the latter.
The term with y is missing, so its coefficient is 0. The equation is 2x + 0y - 5 = 0.
Comparing this with ax + by + c = 0, we get:
a = 2, b = 0, c = -5
