How many linear equations in x and y can be satisfied by x = 2, y = 3?

Let, a = – 1 and b = – 2 then,


ax + by = c


⇒ ( – 1) ×2 + ( – 2) ×3 = – 8


Let, a = 0 and b = 0 then,


ax + by = c


⇒ 0×2 + 0×3 = 0



Let, a = 1 and b = 2 then,


ax + by = c


⇒ 1 × 2 + 2 3 = 8


a



b



c



– 1



– 2



– 8



0



0



0



1



2



8



Since, there can be many solutions for 2a + 3b = c, where a, b and c are constants.


Therefore, there can be infinitely many linear equations in x and y that can be satisfied by x = 2, y = 3

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