A pair of linear equations in two variables x and y

b1x + c1y = a1, c2x + a2y = bhas infinite number of possible solutions if:

1
\(\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}\)
2
\(\dfrac{a_1}{b_2}\ne\dfrac{b_1}{c_2}\)
3
\(\dfrac{b_1}{c_2}=\dfrac{c_1}{a_2}\ne\dfrac{a_1}{b_2}\)
4
\(\dfrac{a_1}{b_2}=\dfrac{b_1}{c_2}=\dfrac{c_1}{a_2}\)

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