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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
In other words, this solution is not suitable for equation (1), but it is true for equation (2),
So we bring in 2, B + a = 19, 3
Similarly, we take x = - 2, y = 4 into ①, - 2A + 4B = 16, ④
③ (4) a = 10, B = 9
The original equation (1) and (2) show that 10x + 9y = 16 (1) and 9x + 10Y = 19 (2)
The solution is x = - 11 / 19, y = 35 / 38
RELATED INFORMATIONS
- 1. 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?
- 2. 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
- 3. 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
- 4. If the degree of cube + 2x Square-1 of polynomial ax is the same as that of 2x-3xb, what conditions should a and B satisfy
- 5. Decomposition factor: (AX by) cubic + (by CZ) cubic - (AX CZ) cubic
- 6. If any two real numbers a and B are taken in the interval [- 2,2], then the probability of two real numbers of X equation x ^ 2 + ax-b ^ 2 + 1 = 0? The equation is: x ^ 2 + 2ax-b ^ 2 + 1 = 0
- 7. In the interval [- 1,1], take any two points a and B, and the probability that the two points of equation x2 + ax + B = 0 are both real numbers is p, then the value range of P is___ ．
- 8. 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______ ．
- 9. 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______ ．
- 10. 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
- 11. 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?
- 12. 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
- 13. 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
- 14. The solution of the system ax + by = 2C CZ + AX = 2B by + CZ = 2A is a. B and C are constant and not 0
- 15. 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
- 16. 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
- 17. Given a ^ 2 + B ^ 2 + C ^ 2 = 1, x ^ 2 + y ^ 2 + C ^ 2 = 9, find the maximum value of AX + by + CZ The answer is 3
- 18. If the solution of the system of equations ax-by-2z = 13, ax + 2Y + CZ = - 2, cx-4y + BZ = 28 is x = 3, y = - 1, z = - 2, find the value of a, B, C
- 19. 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
- 20. Let x-by + CZ, y = CZ + ax, z = ax + by, find the value of a / A + 1 + B / B + 1 + C / C + 1