Question

in the given system of linear equation,2x+y=7 and 4x-3y=-1 the solution(value of x and y) is​

Answer 1

Given Equations :

• 2x + y = 7
• 4x - 3y = -1

To Find : The value of x and y?

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Here, we have two equations :

$\tt{\fbox{2x + y = 7}} - - - - - - [Equation \: No. \: (i)]$

$\tt{\fbox{4x - 3y = -1}} - - - - - - [Equation \: No. \: (ii)]$

From equation no. (ii), we get

$\bf{ : \: \implies \: x = \dfrac{-1 + 3y}{4} }$

Substituting x = $\rm{ \dfrac{-1 + 3y}{4} }$ in equation no. (i), we get

$\sf{ \leadsto 2x + y = 7}$

$\sf{ \leadsto 2 × \dfrac{-1 + 3y}{4} + y = 7}$

$\sf{ \leadsto \dfrac{-1 + 3y}{2} + y = 7}$

$\sf{ \leadsto \dfrac{-1 + 3y + 2y}{2} = 7}$

$\sf{ \leadsto \dfrac{-1 + 5y}{2} = 7}$

$\sf{ \leadsto -1 + 5y = 7 × 2}$

$\sf{ \leadsto 5y = 14 + 1}$

$\sf{ \leadsto y = \dfrac{15}{5} }$

$\sf{ \leadsto y = 3}$

Hence, y = 3.

Substituting y = 3 in equation no. (ii), we get

$\sf{ \mapsto 4x - 3y = -1}$

$\sf{ \mapsto 4x - 3 × 3 = -1}$

$\sf{ \mapsto 4x = -1 + 9}$

$\sf{ \mapsto x = \dfrac{8}{4} }$

$\sf{ \mapsto x = 2}$

Hence, x = 2.

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So, the value x and y is 2 and 3 respectively.