RD Chapter 13 Linear Equations in Two Variables Ex 13.1 Solutions
Question - 1 : - Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:
(i) -2x + 3y = 12 (ii) x – y/2 – 5 = 0 (iii) 2x + 3y = 9.35
(iv) 3x = -7y (v) 2x + 3 = 0 (vi) y – 5 = 0
(vii) 4 = 3x (viii) y = x/2
Answer - 1 : -
(i) Given equation, -2x + 3y = 12
Or – 2x + 3y – 12 = 0
Comparing the given equation with ax + by + c = 0
We get, a = – 2; b = 3; c = -12
(ii) Given equation, x – y/2 – 5= 0
Comparing the given equation with ax + by + c = 0 ,
We get, a = 1; b = -1/2, c = -5
(iii) Given equation, 2x + 3y = 9.35
or 2x + 3y – 9.35 =0
Comparing the given equation with ax + by + c = 0
We get, a = 2 ; b = 3 ; c = -9.35
(iv) Given equation, 3x = -7y
or 3x + 7y = 0
Comparing the given equation with ax+ by + c = 0,
We get, a = 3 ; b = 7 ; c = 0
(v) Given equation, 2x + 3 = 0
or 2x + 0y + 3 = 0
Comparing the given equation with ax + by + c = 0,
We get, a = 2 ; b = 0 ; c = 3
(vi) Given equation, y – 5 = 0
or 0x + y – 5 = 0
Comparing the given equation with ax + by+ c = 0,
We get, a = 0; b = 1; c = -5
(vii) Given equation, 4 = 3x
or 3x + 0y – 4 = 0
Comparing the given equation with ax + by + c = 0,
We get, a = 3; b = 0; c = -4
(viii) Given equation, y = x/2
Or x – 2y = 0
Or x – 2y + 0 = 0
Comparing the given equation with ax + by + c = 0 ,
We get, a = 1; b = -2; c = 0
Question - 2 : - Write each of the following as an equation in two variables:
(i) 2x = -3 (ii) y=3 (iii) 5x = 7/ 2 (iv) y = 3/2x
Answer - 2 : -
(i) Given equation, 2x = -3
The above equation can be written in two variables as,
2x + 0y + 3 = 0
(ii) Given equation, y = 3
The above equation can be written in two variables as,
0 x + y – 3 = 0
(iii) Given equation, 5x = 7/2
The above equation can be written in two variables as,
5x + 0y – 7/2 = 0
or 10x + 0y – 7 = 0
(iv) Given equation, y = 3/2 x
The above equation can be written in two variables as,
2y = 3x
3x – 2y = 0
3x – 2y + 0 = 0
Question - 3 : - The cost of ball pen is Rs 5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.
Answer - 3 : -
Let the cost of a fountain pen be y and cost of a ball pen be x.
According to the given statement,
x = y/2 − 5
or 2x = y – 10
or 2x – y + 10 = 0
Which is required linear equation.