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 ;
(i) We are given
- 2x + 3y = 12
- 2x + 3y - 12 = 0
Comparing the given equation with ax + by + c = O
We get, a = - 2; b = 3; c = -12
(ii) We are given
x - y/2 - 5= 0
Comparing the given equation with ax + by + c = 0,
We get, a = 1; b = – 1/2, c = – 5
(iii) We are given
2x + 3y = 9.35
2x + 3y - 9.35 =0
Comparing the given equation with ax + by + c = 0
We get, a = 2; b = 3; c = - 9.35
(iv) We are given
3x = - 7y
3x + 7y = 0
Comparing the given equation with ax+ by + c = 0,
We get, a = 3; b = 7; c = 0
(v) We are given
2x + 3 = 0
Comparing the given equation with ax + by + c = 0,
We get, a = 2; b = 0; c = 3
(vi) We are given
y - 5 = 0
Comparing the given equation with ax + by + c = 0,
We get, a = 0; b = 1; c = – 5
(vii) We are given
4 = 3x
3x - 4 = 0
Comparing the given equation with ax + by + c = 0,
We get, a = 3; b = 0; c = - 4
(viii) We are given
y = x/2
Taking L.C.M ⟹ x - 2y = 0
Comparing the given equation with ax + by + c = 0,
We get, a = 1; b = – 2; c = 0
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
(i) We are given,
2x = - 3
Now, in two variable forms the given equation will be
2x + 0y + 3 = 0
(ii) We are given,
y = 3
Now, in two variable forms the given equation will be
0 x + y - 3 = 0
(iii) We are given,
5x = – 7/2
Now, in two variable forms the given equation will be
5x + 0y + 7/2 = 0
10x + 0y - 7 = 0
(iv) We are given,
y = 32x (Taking L.C.M on both sides)
Now, in two variable forms the given equation will be
3x - 2y + 0 = 0
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.
Let the cost of fountain pen be y and cost of ball pen be x.
According to the given equation, we have
x = y/2 − 5
⟹ 2x = y - 10
⟹ 2x - y + 10 = 0
Here y is the cost of one fountain pen and x is that of one ball pen.