Multiple choice

Solve the given pair of equations by substitution method: $2a\, +\, 3b\, =\, 6$ $3a\, +\, 5b\, =\, 15$

  1. $a = 3, b = 2$
  2. $a = -15, b = 12$
  3. $a = 8, b = 15$
  4. $a = -7, b = 3$
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B Correct answer
Explanation

Solving 2a + 3b = 6 and 3a + 5b = 15: Multiply the first by 3 and second by 2: 6a + 9b = 18 and 6a + 10b = 30. Subtracting gives b = 12. Substituting b = 12 into 2a + 3(12) = 6 gives 2a = -30, so a = -15.

AI explanation

Using the elimination method, multiply the first equation by 3 to get 6a + 9b = 18, and multiply the second equation by 2 to get 6a + 10b = 30. Subtracting the first modified equation from the second gives b = 12. Substituting b = 12 into the first original equation, 2a + 3b = 6, yields 2a + 36 = 6, which simplifies to 2a = -30 and a = -15.

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