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Solve the following pairs of equations:
$ 43 x+67 y=-24 $
$ 67 x+43 y=24 $
Given:
\( 43 x+67 y=-24 \)
\( 67 x+43 y=24 \)
To do:
We have to solve the given pairs of equations.
Solution:
\( 43 x+67 y=-24 \)......(i)
\( 67 x+43 y=24 \).........(ii)
Multiplying (i) by 43 and (ii) by 67 and subtracting the results, we get,
$43(43x+67y)=43(-24)$
$43^2x+43(67)y=24(-43)$.........(iii)
$67(67x+43y)=67(24)$
$67^2x+43(67)y=24(67)$.......(iv)
Subtracting (iii) from (iv), we get,
$(67^2-43^2)x=24(67+43)$
$(67+43)(67-43)x=24(110)$
$110(24)x=24(110)$
$x=1$
This implies,
$43(1)+67y=-24$
$67y=-24-43$
$67y=-67$
$y=-1$
Therefore,
$x=1$
$y=-1$
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