MP Board Class 9th Maths Solutions Chapter 4 Linear Equations in Two Variables Ex 4.1
Question 1.
The cost of notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
Solution:
Let cost of pen be ₹ x and cost of a notebook be ₹ y
y = 2x
y – 2x = 0.
Question 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 = 9.3\(\overline { 5 } \)
- x – \(\frac{y}{5}\) – 10 = 0
- -2x + 3y = 6
- x = 3y
- 2x = – 5y
- 3x + 2 = 0
- y – 2 = 0
- 5 = 2x
Solution:
1. 2x + 3y = 9.3\(\overline { 5 } \)
2x + 3y – 9.3\(\overline { 5 } \) = 0
a = 2, b = 3, c = – 9.3\(\overline { 5 } \)
2. x – \(\frac{y}{5}\) – 10 = 0
a = 1, b = – \(\frac{1}{5}\), c = – 10
3. -2x + 3y = 6
– 2x + 3y – 6 = 0
a = – 2, b = 3, c = – 6
4. x = 3y
1. x – 3y + 0 = 0
a – 1, b = – 3, c = 0
5. 2x = – 5y
2x + 5y + 0 = 0
a = 2, b = 5, c = 0
6. 3x + 2 = 0
3x + 0y + 2 = 0
a = 3, b = 0, c = 2
7. y – 2 = 0
0x + y – 2 = 0
a = 0, b = 1, c = – 2
8. 5 = 2x
– 2x + 0y + 5 = 0
a = – 2, b = 0, c = 5
Solution of a Linear Equation:
Consider a Linear equation x + 2y = 6
Let x = 2 and y = 2.
Then L.H.S. of the equation = x + 2y = 2 + 2 x 2 = 6
and R.H.S. of the equation = 6 (given)
i.e., LHS. = R.H.S. for x = 2 and y = 2.
Therefore, x = 2 and y = 2 i.e., (2, 2) is the solution of the given equation x + 2y = 6.
Any pair of values of x and y which satisfies the given equation is called a solution of the equation. A linear equation in two variables has infinitely many solutions.
Note:
To find the solution of an equation, assure a value of one of the variable and calculate the value of second variable from the given equation.