Question
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :$\frac{x-y}{6}=2(4-x);2 x+y=3(x-4)$
✓
Answer
The given pair of linear equations are
$ \frac{x-y}{6}=2(4-x)$
$ \Rightarrow x-y=12(4-x)$
$ \Rightarrow x-y=48-12 x$
$\Rightarrow 13 x-y=48\dots....(1) [$ On simplifying$]$
$ 2 x+y=3(x-4)$
$ \Rightarrow 2 x+y=3 x-12$
$\Rightarrow x-y=12\dots.....(2) [$ On simplifying $]$
Multiply equation $(2)$ by $13$ , We get,
$13 x-13 y=156\dots .....(3)$
Multiply equation $(2)$ by $13 ,$ We get,
$13 x-13 y=156$
Subtracting equation $(1)$ from $(3)$
$13 x-13 y=156$
$- 13 x-y=48$
$-+y$
$-12 y=108$
$y=-9$
Substituting $y=-9$ in equation $(1)$, we get
$13 x-(-9)=48$
$ \Rightarrow 13 x=39$
$ \Rightarrow x=3$
$\therefore$ Solution is $x=3$ and $y=-9$.
$ \frac{x-y}{6}=2(4-x)$
$ \Rightarrow x-y=12(4-x)$
$ \Rightarrow x-y=48-12 x$
$\Rightarrow 13 x-y=48\dots....(1) [$ On simplifying$]$
$ 2 x+y=3(x-4)$
$ \Rightarrow 2 x+y=3 x-12$
$\Rightarrow x-y=12\dots.....(2) [$ On simplifying $]$
Multiply equation $(2)$ by $13$ , We get,
$13 x-13 y=156\dots .....(3)$
Multiply equation $(2)$ by $13 ,$ We get,
$13 x-13 y=156$
Subtracting equation $(1)$ from $(3)$
$13 x-13 y=156$
$- 13 x-y=48$
$-+y$
$-12 y=108$
$y=-9$
Substituting $y=-9$ in equation $(1)$, we get
$13 x-(-9)=48$
$ \Rightarrow 13 x=39$
$ \Rightarrow x=3$
$\therefore$ Solution is $x=3$ and $y=-9$.
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