Theory question 105
Linear and Simultaneous Equations(a) Solve the simultaneous equations 3y − 2x = 21; 4y + 5x = 5.
(b) Six identical cards numbered 1–6 are placed face down. A card is to be picked at random. A person wins $60.00 if he picks the card numbered 6. If he picks any of the other cards, he loses $10.00 times the number on the card. Calculate the probability that he: (i) loses (ii) loses $20.00.
Show the model answer
Model answer
(a) Multiply the first by 5 and the second by 2: 15y − 10x = 105 and 8y + 10x = 10. Add: 23y = 115, y = 5.
Then 2x = 3(5) − 21 = −6, x = −3.
(b)(i) He loses with any card from 1 to 5: P = 5/6.
(ii) He loses $20 only with card 2: P = 1/6.
Explanation
Make the x coefficients equal and opposite, then add.