(Q.29). Check whether the following equations are consistent or inconsistent. Solve them graphically

3
2
 x +
5
3
 y = 7

9x – 10y = 12

Given pair of equations
3
2
 x +
5
3
 y = 7 and 9x – 10y = 12
Now take
3
2
 x +
5
3
 y = 7 ⇒
x + y
 = 7 ⇒ x + y =

and 9x – 10y =12

a1
a2
 =
=
;
b1
b2
 =
-
 =
-
and
c1
c2
 =
-
-
 =
Since
a1
a2
 ≠
b1
b2
 they are intersecting lines and hence consistent pair of linear equations.
9x + 10y = 42
x 0 1 -1 3
y
9x – 10y = 12
x 0 1 -1 -2
y - - - -

The unique solution of given pair of equations is (, )