Question

iii) 4x + y = 11 and 7x - 2y = 8 by elimination method​

Answer 1

Answer:

x=2 and y=3

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Answer 2

$\large\underline{\sf{Solution-}}$

Given pair of linear equation are

$\rm :\longmapsto\:4x + y = 11 - - - (1)$

and

$\rm :\longmapsto\:7x - 2y = 8 - - - (2)$

Now,

Multiply equation (1) by 2, we get

$\rm :\longmapsto\:8x + 2y = 22 - - - (2)$

Now,

On adding equation (2) and equation (3), we get

$\rm :\longmapsto\:7x - 2y + 8x + 2y =8 + 22$

$\rm :\longmapsto\:15x =30$

$\bf\implies \:x = 2$

On substituting x = 2, in equation (1), we get .

$\rm :\longmapsto\:4(2) + y = 11$

$\rm :\longmapsto\:8 + y = 11$

$\rm :\longmapsto\: y = 11 - 8$

$\bf\implies \:y = 3$

Hence,

Solution of pair of linear equation

$\rm :\longmapsto\:4x + y = 11$

and

$\rm :\longmapsto\:7x - 2y = 8$

is

$\red{\boxed{ \bf{x = 2 \: \: \: and \: \: \: y = 3}}}$

Additional Information :-

Let's solve the same pair of linear equations by substitution method.

Given equations are

$\rm :\longmapsto\:4x + y = 11 - - - (1)$

and

$\rm :\longmapsto\:7x - 2y = 8 - - - (2)$

From equation (1), we have

$\rm :\longmapsto\:4x + y = 11$

$\bf\implies \:y = 11 - 4x - - - (3)$

On substituting the value of y in equation (2), we get

$\rm :\longmapsto\:7x - 2(11 - 4x) = 8$

$\rm :\longmapsto\:7x - 22 + 8x = 8$

$\rm :\longmapsto\:15x = 8 + 22$

$\rm :\longmapsto\:15x = 30$

$\bf\implies \:x = 2$

On substituting the values of x, we get

$\rm :\longmapsto\:y = 11 - 4 \times 2$

$\rm :\longmapsto\:y = 11 - 8$

$\bf\implies \:y = 3$