Multiple choice

Solve the following pair of equations $31x-42y=51; \, \, 42x-31y=95$

  1. $x=3, \, y=1$
  2. $x=2, \, y=1$
  3. $x=1, \, y=1$
  4. $x=6, \, y=1$
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A Correct answer
Explanation

Substitute x=3 and y=1 into the equations. For the first: 31(3) - 42(1) = 93 - 42 = 51. For the second: 42(3) - 31(1) = 126 - 31 = 95. Both equations are satisfied.

AI explanation

Adding the two equations, 31x - 42y = 51 and 42x - 31y = 95, yields 73x - 73y = 146. Dividing by 73 simplifies this to x - y = 2. Subtracting the first equation from the second gives 11x + 11y = 44, which simplifies to x + y = 4. Solving x - y = 2 and x + y = 4 results in x = 3 and y = 1.

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