For the system of linear equations
\(x + y + z = 5000\)
\(6x + 7y + 8z = 35800\)
\(6x + 7y - 8z = 7000\)
the values of \(x, y\) and \(z\) are:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(x = 1000;\ y = 2200;\ z = 1800\)
The second and third equations differ only in the sign of 8z, so subtracting them removes x and y:
\((6x + 7y + 8z) - (6x + 7y - 8z) = 35800 - 7000\)
\(16z = 28800\)
\(z = 1800\)
Putting z = 1800 in the first two equations:
\(x + y = 3200\)
\(6x + 7y = 35800 - 14400 = 21400\)
Subtracting 6 times the first of these from the second:
\(y = 21400 - 19200 = 2200\)
\(x = 3200 - 2200 = 1000\)
So x = 1000, y = 2200 and z = 1800.