Question
Solve the following simultaneous equations by the substitution method$:\ 13 + 2y = 9x,3y = 7x$
✓
Answer
The given equations are
$ 13+2 y=9 x ....(i)$
$3 y=7 x ....(ii) $
Now, consider equation
$ 3 y=7 x$
$\Rightarrow y=\frac{7}{3} x ....(iii) $
Substituting the value of $y$ in eqn. $(i),$
we get $13+2\left(\frac{7}{3} x\right)=9 x$
$\Rightarrow 13+\frac{14}{3} x=13$
$\Rightarrow 9 x-\frac{14}{3} x=13$
$\Rightarrow \frac{27 x-14 x}{3}=13$
$\Rightarrow 13 x=39$
$\Rightarrow x=\frac{39}{13}$
$=3 $
Putting the value of $x$ in eqn. $(iii),$
we get $y=\frac{7}{3} \times 3$
$=7$
Thus, the solution set is $(3,7)$.
$ 13+2 y=9 x ....(i)$
$3 y=7 x ....(ii) $
Now, consider equation
$ 3 y=7 x$
$\Rightarrow y=\frac{7}{3} x ....(iii) $
Substituting the value of $y$ in eqn. $(i),$
we get $13+2\left(\frac{7}{3} x\right)=9 x$
$\Rightarrow 13+\frac{14}{3} x=13$
$\Rightarrow 9 x-\frac{14}{3} x=13$
$\Rightarrow \frac{27 x-14 x}{3}=13$
$\Rightarrow 13 x=39$
$\Rightarrow x=\frac{39}{13}$
$=3 $
Putting the value of $x$ in eqn. $(iii),$
we get $y=\frac{7}{3} \times 3$
$=7$
Thus, the solution set is $(3,7)$.
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