# If $3 x+2 y=5,2 x-3 y=7$, then the linear equations are a) consistent b) inconsistent c) both (a) & (b) d) none of these

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If $3 x+2 y=5,2 x-3 y=7$, then the linear equations are

a) consistent

b) inconsistent

c) both (a) & (b)

d) none of these

by (45.8k points)

The correct option is (a) consistent

3x + 2y = 5 ...(i)

2x - 3y = 7 ...(ii)

From equation (i) and (ii),

The following pair of linear equations 3x + 2y = 5 = 0 and 2x - 3y = 7 have a unique solution.

Therefore, our system is consistent.