Question

x+2y=10 &2x-4y=-4 pair of equation in two variable​

Answer 1

☯GIVEN :

• $\bf{x +2y = 10}$ and $\bf{2x-4y = -4}$

☯TO DO :

• Solve by Elimination Method.

➲SOLUTION :

▪Multiply the first equation by 2 :

$\implies{ \sf2(x + 2y) = 10 \times 2}$

$\implies{ \bf2x +4y = 20 - (i)}$

▪Multiply the second equation by 1:

$\implies{ \sf 1(2x - 4y) = -4 \times 1}$

$\implies{ \bf 2x - 4y = -4 - (ii)}$

▪Now, Adding both equations :

$\implies \sf(2x + 4y) + (2x - 4y) = 20 + (-4)$

$\implies \sf2x + 4y + 2x - 4y = 20 - 4$

$\implies \sf2x + 2x + \cancel{4y }- \cancel{4y }= 16$

$\implies \sf2x + 2x = 16$

$\implies \sf 4x = 16$

$\implies \sf x = \cancel{\dfrac{16}{4} }$

$\implies \huge{ \underline{\boxed{ \purple{\frak {x = 4 }}}}}$

✞Substituting the obtained value of x in the first equation :

$\implies \sf {x +2y = 10}$

$\implies \sf 4 + 2y = 10$

$\implies \sf 2y = 10 - 4$

$\implies \sf 2y = 6$

$\implies \sf y = \cancel{\dfrac{6}{2}}$

$\implies\huge{ \underline{\boxed{ \purple{ \frak {y = 3 }}}}}$

$\huge{\pink{\therefore}}$ The value of x and y is 4 and 3 respectively.