7 = 2x
⇒ 2x – 7 = 0
⇒ 2x + 0y – 7 = 0
Comparing with ax + by + c = 0, we get
a = 2
b = 0
c = –7
Find solutions of the form x = a, y = 0 and x = 0, y = b for the following pairs of equations. Do they have any common such solution?
3x + 2y = 6 and 5x + 2y = 10
3x + 2y = 6
Put y = 0, we get 3x + 2(0) = 6
3x = 6
(0, 3) is a solution
5x + 2y = 10
Put y = 0, we get 5x + 2(0) = 10
5x = 10
(0, 5) is a solution.
The given equations have a common solution (2, 0)
Find at least 3 solutions for the following linear equation in two variables:
2x + 5y = 13
2x + 5y = 13
5y = 13 - 2x
Put x = 0, then
Put x = 1, then
Put x = 2, then
Put x = 3, then
are the solutions of equation 2x + 5y = 13.
Write each of the following as an equation in two variables:
(i) x = – 5 (ii) y = 2
(iii) 2x = 3 (iv) 5y = 2.
Solution not provided.
Ans. (i) 1 x + 0y + 5 = 0
(ii) 0x + 1y - 2 = 0
(iii) 2x + 0y - 3 = 0
(iv) 0x + 5y - 2 = 0
Solution not provided.
Ans. (i) 2X + 3Y - 4.37 = 0; a = 2, b = 3 and c = - 4.37
(ii) x - - 4 = 0; s = 1, b = c = -4
(iii) - 5x + 3y + 4 = 0; a = -5, b = 3 and c = 4
or
5x - 3y - 4 = 0; a = 5, b = 3 and c = -4
(iv) 2x - y + 0 = 0; a = 2, b = -1 and c = 0