JAMB 1989 · UME · Q23

Linear & simultaneous equations

Solve the pair of equations $2x^{-1} - 3y^{-1} = 4$ and $4x^{-1} + y^{-1} = 1$ for $x$ and $y$ respectively.

Worked solution (try it first)

Let $u = \frac1x$ and $v = \frac1y$ .
The equations become $2u - 3v = 4$ and $4u + v = 1$ .
From the second, $v = 1 - 4u$ .
Substitute: $2u - 3 + 12u = 4$ , so $14u = 7$ and $u = \frac12$ .
Then $v = 1 - 2 = -1$ .
Turn back: $x = \frac1u = 2$ and $y = \frac1v = -1$ .
So $x$ and $y$ are $2, -1$ , option D.

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