If 15x + 4y = 10 and 3x + 2y = 20, then which of the following is the largest? A. 9x + 6y B. 18x + 6y C. 30x + 8y D. 60x + 16y E. 30

(A) The fastest way to solve this question is to see that the expressions in the answer choices A – D can be made of the expressions in the question statement. So we don’t need to find the actual values of x and y in this case. (A) 9x + 6y = 3 × (3x + 2y) = 3 × 20 = 60 (B) 18x + 6y = (15x + 4y) + (3x + 2y) = 10 + 20 = 30 (C) 30x + 8y = 2 × (15x + 4y) = 2 × 10 = 20 (D) 60x + 16y = 4 × (15x + 4y) = 4 × 10 = 40 (E) 30 The correct answer is A.

Solving the original system of equations to find x and y is also an option. Multiplying second equation by 5 we get 10y + 15x = 100. Subtracting first equation we get: 10y – 4y + 15x – 15x = 100 – 10 6y = 90 y = 15 Substituting y into second equation we can find x: 2 × 15 + 3x = 20 3x = -10 x = -10/3 Now we can calculate all of the answer choices: (A) 9x + 6y = 6 × 15 + 9 × (-10/3) = 90 – 30 = 60 (B) 18x + 6y = 6 × 15 + 18 × (-10/3) = 90 – 60 = 30 (C) 30x + 8y= 8 × 15 + 30 × (-10/3) = 120 – 100 = 20 (D) 60x + 16y= 16 × 15 + 60 × (-10/3) = 240 – 200 = 40 (E) 30 60 is the largest. The answer is (A). ---------- I got this problem wrong and I don't know why, can you please help me understand. Following are the steps taken by me.

Consider the first equation as is. Multiply 2nd equation by 2. We get 15x + 4y = 10 6x + 4y =40

Subtracting we get => 9x = -30 And x is negative. What is it that I am doing wrong here??

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