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Mathematics
Mathematics
Problem
State the condition on the ratios
a
1
a
2
,
b
1
b
2
\dfrac{a_1}{a_2},\,\dfrac{b_1}{b_2}
a
2
a
1
,
b
2
b
1
and
c
1
c
2
\dfrac{c_1}{c_2}
c
2
c
1
for the pair of linear equations
a
1
x
+
b
1
y
+
c
1
=
0
a_1x + b_1y + c_1 = 0
a
1
x
+
b
1
y
+
c
1
=
0
and
a
2
x
+
b
2
y
+
c
2
=
0
a_2x + b_2y + c_2 = 0
a
2
x
+
b
2
y
+
c
2
=
0
to have infinitely many solutions.
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