Multiple choice

Solve the given pair of equations by substitution method: $x\, +\, 5y\, =\, 18$ $3x\, +\, 2y\, =\, 41$

  1. $(13 , 1)$
  2. $(1 , 3)$
  3. $(12 , 17)$
  4. $(9 , 16)$
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A Correct answer
Explanation

From x + 5y = 18, x = 18 - 5y. Substitute into 3x + 2y = 41: 3(18 - 5y) + 2y = 41 => 54 - 15y + 2y = 41 => -13y = -13 => y = 1. Then x = 18 - 5(1) = 13. The solution is (13, 1).

AI explanation

From the first equation, x = 18 - 5y. Substituting this into the second equation gives 3(18 - 5y) + 2y = 41. Expanding and simplifying gives 54 - 15y + 2y = 41, which means 13y = 13 and y = 1. Substituting y = 1 into the expression for x gives x = 18 - 5(1) = 13, so the solution is (13, 1).

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