Question

x + y = 5 , 2x - 3y = 4 solve this equation with elimination ,substitution ,cross-multiplication method
$elimination \:$

Answer 1

Now I solved the question

Answer 2

Answer:

$x =\frac{19}{5},\\y=\frac{6}{5}$

Step-by-step explanation:

Substitute method:

Given pair of linear equations:

x+y = 5 => x = 5-y ---(1)

2x-3y=4 ---(2)

Substitute x = 5-y in equation (2), we get

=> 2(5-y)-3y = 4

=> 10-2y-3y = 4

=> 10-5y=4

=> -5y = 4-10

=> -5y = -6

$\implies y = \frac{-6}{-5}\\=\frac{6}{5}$

Substitute y in equation (1), we get

$\implies x = 5-\frac{6}{5}\\=\frac{25-6}{5}\\=\frac{19}{5}$

Therefore,

$x =\frac{19}{5},\\y=\frac{6}{5}$

Elemination method:

x+y=5 ---(1)

2x-3y=4---(2)

/* Multiply equation (1) by 3 ,and add to equation (2) ,we get */

2x-3y=4

3x+3y = 15

_______________

5x = 19

_______________

$x = \frac{19}{5}$

\* Put x value in equation (1), we get

$\frac{19}{5}+x =5$

$\implies y= 5-\frac{19}{5}$

$\implies y = \frac{25-19}{5}$

$\implies y = \frac{6}{5}$

Therefore,

$x =\frac{19}{5},\\y=\frac{6}{5}$

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