Question

using elimination method solve 5x+4y=11,3x+5y=4

The answer should be (3,-1)​

Answer 1

Answer:

Please see the attachment for answer with complete solution

Step-by-step explanation:

thank you.

Answer 2

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

Given pair of linear equations is

$\rm :\longmapsto\:5x + 4y = 11 - - - - (1)$

and

$\rm :\longmapsto\:3x + 5y = 4 - - - - (2)$

Now, multiply equation (1) by 3 and equation (2) by 5, we get

$\rm :\longmapsto\:15x + 12y = 33 - - - - (3)$

and

$\rm :\longmapsto\:15x + 25y = 20 - - - - (4)$

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

$\rm :\longmapsto\: - 13y = 13$

$\bf\implies \:\boxed{ \tt{ \: y \: = \: - \: 1 \: }}$

On substituting the value of y in equation (1), we get

$\rm :\longmapsto\:5x + 4( - 1) = 11$

$\rm :\longmapsto\:5x - 4 = 11$

$\rm :\longmapsto\:5x = 11 + 4$

$\rm :\longmapsto\:5x = 15$

$\bf\implies \:\boxed{ \tt{ \: x \: = \: 3 \: }}$

Hence,

$\red{\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{x \: = \: 3 \: } \\ \\ &\sf{y \: = \: - \: 1} \end{cases}\end{gathered}\end{gathered}}$

Verification :-

Consider the equation,

$\rm :\longmapsto\:3x + 5y = 4$

On substituting the values of x and y, we get

$\rm :\longmapsto\:3(3) + 5( - 1) = 4$

$\rm :\longmapsto\:9 - 5 = 4$

$\rm :\longmapsto\:4 = 4$

Hence, Verified