If 7 x+11 y=1 and 8 x+13 y=2 , then the values of x and y are:

The correct answer is Option (3) → \(-3,2\)

Make the x-terms of the two equations equal, then subtract so that x cancels and y can be found.

• \(7x+11y=1\)        (1)

• \(8x+13y=2\)        (2)

• 8 × (1): \(56x+88y=8\)        (3)

• 7 × (2): \(56x+91y=14\)        (4)

• Subtracting (3) from (4), the x terms cancel: \(3y=6\), so \(y=2\)

• Putting \(y=2\) in (1): \(7x+22=1\), so \(x=-3\)

Shortcut:

• Put each option into equation (1): only \((-3,2)\) gives \(-21+22=1\)

• It satisfies equation (2) as well: \(-24+26=2\)