Xiao Ming and Xiao Liang solve the same system of equations (1) ax + by = 1 (2) BX + ay = - 5. Xiao Ming miscopies (1) and gets the solution as x = - 1, y = 3; while Xiao Liang miscopies (2) and gets the solution as x = 3, y = 2. Can you correctly find the solution of the original system of equations according to the above results? | Math enthusiast | Mathematical art

Xiao Ming and Xiao Liang solve the same system of equations (1) ax + by = 1 (2) BX + ay = - 5. Xiao Ming miscopies (1) and gets the solution as x = - 1, y = 3; while Xiao Liang miscopies (2) and gets the solution as x = 3, y = 2. Can you correctly find the solution of the original system of equations according to the above results?

In this way, Xiaoming copied the wrong solution of (1) and got the solution as x = negative 1, y = 3. That is to say, there is no wrong solution of (2) BX + ay = - 5, x = negative 1, y = 3 is the solution of (2) BX + ay = - 5. Similarly, Xiaoliang copied the wrong solution of (2), then x = 3, y = 2 is the solution of (1) ax + by = 1, so there is - B + 3A = - 5, 3A + 2B = 1, and a = - 1, B = 2, so the original equation is - x + 2Y = 1 2x - y = - 5

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1. To solve the system of equations ax + by = 16 BX + ay = 19, Xiaoming gets x = 1y = 7 and Xiaoliang gets x = - 2Y = 4. To solve the system of equations ax + by = 16 BX + ay = 19, Xiaoming gets x = 1y = 7 and Xiaoliang gets x = - 2Y = 4, how about finding the correct solution and the original equation? As of 10 o'clock, speed answer
2. It is known that ax + by = 7, ax's square + by's Square = 49, ax's cube + by's cube = 133, ax's fourth power + by's fourth power = 406 Find the value of 17 (a + b) of 1999 (x + y) + 6xy-2
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7. If the real numbers a and B satisfy A2 + B2 ≤ 1, then the probability of the equation x2-ax + 34b2 = 0 with real roots is zero______ ．
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9. F (x) = ax + BX + 1 (a, B ∈ R) if f (- 1) = 0 and f (x) ≥ 0 for any real number x, the expression of F (x) is obtained F (x) = ax + BX + 1 (a, B ∈ R) ① if f (- 1) = 0 and f (x) ≥ 0 for any real number x, the expression for finding f (x) holds. ② under the condition of ①, when x ∈ [- 2,2], G (x) = f (x) - KX is a monotone increasing function, the value range of real number k can be found
10. The equation | x ^ 2 + ax + B | = 2 of X has three different real numbers, and the three different real numbers are exactly three sides of a right triangle. Find the right triangle
11. In the system of equations ax + by = 16 1 BX + ay = 19 2, copy 1 wrong to x = 1 y = 1, Xiao Liang copy 2 wrong to x = - 2 y = 4 to find the correct answer 16 and 1 are separated, 1 with a table, 19 and 2 are also not good oral expression
12. When solving the equations {ax + by = 16 ① BX + ay = 19 ②, Xiao Ming copied the equation ① wrong and got the wrong solution {x = 1, y = 7), while Xiao Liang copied the equation ② wrong What is the original system of equations?
13. If the solution of the system of equations ax-by-2z = 13 ax + 2Y + CZ = - 2 about X, y and Z is x = 3, y = - 1, z = - 2, cx-4y + BZ = 31, the value adding process of a, B and C is obtained
14. Take any point P in the interior or boundary of △ ABC, and note that the distances from P to three sides a, B, C are x, y, Z in turn. Prove that ax + by + CZ is a constant
15. The solution of the system ax + by = 2C CZ + AX = 2B by + CZ = 2A is a. B and C are constant and not 0
16. If the solutions of the equations ax by = 8, cy BZ = 1, 2bx + CZ = 5 are x = 1, y = - 2, z = - 1, then what is the number of ABC
17. Given a & sup2; + B & sup2; + C & sup2; = 1, X & sup2; + Y & sup2; + Z & sup2; = 1, prove ax + by + CZ ≤ 1 It's easy to understand
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20. It is known that {x = 1, {y = 2, {z = 3, are the solutions of the equations {ax + by = 2, {by + CZ = 3, {CX + AZ = 7, and the value of a + B + C is obtained