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Solve the pair of linear equations:
3x $+$ 2y = 4
4x $+$ 6y = 2
Given: 3x $+$ 2y = 4 ...(i)
4x $+$ 6y = 2 ...(ii)
To find: We have to find x from the given equations.
Solution:
Multiplying eq (i) with 3:
$3( 3x\ +\ 2y) \ =\ 3( 4)$
$9x\ +\ 6y\ =\ 12$ ...(iii)
Subtracting eq (ii) from eq (iii)
$9x\ +\ 6y\ -\ ( 4x\ +\ 6y) \ =\ 12\ -\ 2$
$9x\ +\ 6y\ -\ 4x\ -\ 6y\ =\ 12\ -\ 2$
$5x\ \ =\ 10$
$x\ \ =\ \frac{10}{5}$
$x\ =\ 2$
Putting value of x in eq (i)
3(2) $+$ 2y = 4
6 $+$ 2y = 4
2y = 4 $-$ 6
2y = $-$ 2
y = $-$ $\frac{2}{2}$
y = $-$1
So, solution to the given equations is x=2 and y=$-$1.
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