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Mathematics
Problem
Find the value of
λ
\lambda
λ
, if the following equations are consistent
x
+
y
−
3
=
0
(
1
+
λ
)
x
+
(
2
+
λ
)
y
−
8
=
0
x
−
(
1
+
λ
)
y
+
(
2
+
λ
)
=
0
\begin{aligned} x + y - 3 &= 0 \\ (1+\lambda)x + (2+\lambda)y - 8 &= 0 \\ x - (1+\lambda)y + (2+\lambda) &= 0 \end{aligned}
x
+
y
−
3
(
1
+
λ
)
x
+
(
2
+
λ
)
y
−
8
x
−
(
1
+
λ
)
y
+
(
2
+
λ
)
=
0
=
0
=
0
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