(Q.15). Check each of the given systems of equations to see if it has a unique solution, infinitely many solutions or no solution. Solve them graphically.

2x + 3y = 1

3x – y = 7

Let a1x + b1y – c1 = 0 ≃ 2x + 3y – 1 = 0

a2x + b2y + c2 = 0 ≃ 3x – y – 7 = 0

Now comparing their coefficients i.e.,
a1
a2
 and
b1
b2
⇒
2
 ≠
-1

The given lines are intersecting lines.

2x + 3y = 1

3y = 1 – 2

y =
1 - 2x
2x + 3y = 1
x y =
1 - 2x
3
 		(x,y)
5 - (5,-)
-1 (-1,)

3x - y = 7

y = 3x -

3x - y - 7 = 0
x y = 3x - 7 (x,y)
0 - (0,-)
3 (3,)

The system of equations has a unique solution (, – ).