Question

Solve by elimination method
2x+3y=5,3x+4y=7

Answer 1

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

Given pair of linear equation is

$\rm :\longmapsto\:2x + 3y = 5 - - - (1)$

and

$\rm :\longmapsto\:3x + 4y = 7 - - - (2)$

Multiply equation (1) by 3 and equation (2) by 2, we get

$\rm :\longmapsto\:6x + 9y = 15 - - - - (3)$

and

$\rm :\longmapsto\:6x + 8y = 14 - - - - (4)$

On Subtracting equation (4) from equation (3), we get

$\rm \implies\:y = 1$

On substituting y = 1, in equation (1), we get

$\rm :\longmapsto\:2x + 3(1) = 5$

$\rm :\longmapsto\:2x + 3 = 5$

$\rm :\longmapsto\:2x = 5 - 3$

$\rm :\longmapsto\:2x = 2$

$\rm \implies\:x = 1$

So, Solution of pair of linear equations is

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{x = 1} \\ \\ &\sf{y = 1} \end{cases}\end{gathered}\end{gathered}$

VERIFICATION

Consider equation (1)

$\rm :\longmapsto\:2x + 3y = 5$

On substituting the values of x and y, we get

$\rm :\longmapsto\:2(1) + 3(1) = 5$

$\rm :\longmapsto\:2 + 3 = 5$

$\rm :\longmapsto\:5= 5$

Hence, Verified

Consider Equation (2)

$\rm :\longmapsto\:3x + 4y = 7$

On substituting the values of x and y, we get

$\rm :\longmapsto\:3(1) + 4(1) = 7$

$\rm :\longmapsto\:3 + 4 = 7$

$\rm :\longmapsto\:7 = 7$

Hence, Verified