A pair of linear equations which has a unique solution x = 2, y = –3 is ______.

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A pair of linear equations which has a unique solution x = 2, y = –3 is 2x + 5y = –11, 4x + 10y = –22 and x – 4y –14 = 0, 5x – y – 13 = 0. Explanation: For option (A), L.H.S. = x + y = 2 + (-3) = −1 = R.H.S. and L.H.S. = 2x − 3y = 2(2) − 3(−3) = 4 + 9 = 13 $\neq$ R.H.S. :. does not satisfy the equation. For option (B), L.H.S. = 2x + 5y = 2(2) + 5(−3) = 4 − 15 = −11 = R.H.S. and L.H.S. = 4x + 10y = 4(2) + 10(−3) = 8 − 30 = −22 = R.H.S. Since x = 2, y = −3 satisfy the equations in option (B). x = 2, y = −3 is a unique solution of these equations. For option (C), L.H.S. = 2x − y = 2(2) − (−3) = 4 + 3 = 7 $\neq$ R.H.S. and L.H.S. = 3x + 2y = 3(2) + 2(−3) = 6 − 6 = 0 = R.H.S. x = 2, y = −3 does not satisfy the equation. For option (D), L.H.S. = x − 4y − 14 = 2 − 4 (−3) −14 = 2 + 12 − 14 = 14 − 14 = 0 = R.H.S. and L.H.S. = 5x − y − 13 = 5(2) − (−3) − 13 = 10 + 3 − 13 = 0 = R.H.S. x = 2, y = −3 satisfy the equations in option (D)

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