Solve the following simultaneous equations by the substitution me… - Vidyadip

Question

Solve the following simultaneous equations by the substitution method:$5x + 4y - 23 = 0,x + 9 = 6y$

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Answer

The given equations are
$ 5 x+4 y-23=0\dots ....(i)$
$x+9=6 y\dots ....(ii) $
Now, consider equation
$ x+9=6 y$
$\Rightarrow x=6 y-9\dots ....(iii) $
Substituting the value of $x$ in eqn. $(i),$ we get
$ 5(6 y-9)+4 y-23=0$
$\Rightarrow 30 y-45+4 y-23=0$
$\Rightarrow 34 y-68=0$
$\Rightarrow 34 y=68$
$\Rightarrow y=\frac{68}{34}=2 $
Putting the value of $y$ in eqn. $(iii),$ we get
$ x=6(2)-9$
$=12-9$
$=3 $
Thus, the solution set is $(3,2)$.

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