(Q.31). Check whether the following equations are consistent or inconsistent. Solve them graphically
4
3
x +
2y = 8
2x + 3y = 12
Given pair of equations
4
3
x +
2y = 8 ⇒
x +
y
3
= 8 ⇒
x +
y =
⇒
x +
y =
a
1
a
2
=
=
;
b
1
b
2
=
=
;
c
1
c
2
=
=
∴
a
1
a
2
=
b
1
b
2
=
c
1
c
2
Thus the equations are consistent.
∴ The given equations have infinitely many solutions.
4x + 6y = 24
x
y
(x,y)
0
(0,
)
6
(6,
)
9x – 10y = 12
x
y
(x,y)
0
(0,
)
6
(6,
)
Clear
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