Theory question 102
Linear and Simultaneous Equations(a) Solve the following pair of simultaneous equations
2x + 5y = 6½
5x − 2y = 9
(b) If log10(2x + 1) − log10(3x − 2) = 1, find x
Show the model answer
Model answer
(a) Double the first equation: 4x + 10y = 13. Multiply the second by 5: 25x − 10y = 45
Add: 29x = 58, so x = 2
Substitute: 4 + 5y = 6½, so y = ½
(b) log10[(2x + 1)/(3x − 2)] = 1 = log1010
(2x + 1)/(3x − 2) = 10, so 2x + 1 = 30x − 20
28x = 21, x = ¾ (check: 3x − 2 = ¼ > 0, so the log exists)
Explanation
Use the subtraction law of logarithms to combine the left-hand side into one log.