Multiple choice

Solve the following pair of simultaneous equations: $a\, =\, b\, +\, 2$ $2a\, -\, b\, =\, 7$

  1. $a = -2, b = 9$
  2. $a = 12, b = 6$
  3. $a = -3, b = 7$
  4. $a = 5, b = 3$
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D Correct answer
Explanation

Substitute a = b + 2 into 2a - b = 7: 2(b+2) - b = 7 => 2b + 4 - b = 7 => b = 3. Then a = 3 + 2 = 5.

AI explanation

Substitute the value a = b + 2 from the first equation into the second equation to get 2(b + 2) - b = 7. Simplifying this gives 2b + 4 - b = 7, which results in b = 3. Substituting b = 3 back into the first equation yields a = 3 + 2, giving a = 5.

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