Question

Solve the following simultaneous equation using either the substitution method or the elimination method, showing all the necessary steps.
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Answer 1

Answer:

$x=1\frac{83}{91}\\y=-2\frac{73}{91}$

Step-by-step explanation:

#Using the method of substitution and replacement of unknown values.

Given that

$\frac{3}{2}x+\frac{2}{3}y=1...(i)\\and\\\frac{1}{6}x-\frac{3}{5}y=2...(ii)$

Express eqtn (ii) in terms of x

$\frac{1}{6}x=2+\frac{3}{5}y\\x=12+\frac{18}{5}y$

Replacing for x in eqtn (i)

$\frac{3}{2}(12+\frac{18}{5}y)+\frac{2}{3}y=1\\18+\frac{27}{5}y+\frac{2}{3}y=1\\18-1=-\frac{91}{15}y\\y=-2\frac{73}{91}$

Substitute y value in eqtn(ii) to obtain x

$Y=-2\frac{73}{91}\\\frac{1}{6}x-\frac{3}{5}y=2\\x=2+\frac{3}{5}(-2\frac{73}{91})\\x=1\frac{83}{91}$