Question

solve by elimination method:x-y=5, 2x-3y=5​

Answer 1

Given

equations : Given pair of equations:

x + y = 5 \: ---(1)x+y=5−−−(1)

and \: 2x - 3y = 4 \: ---(2)and2x−3y=4−−−(2)

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

$3x + 3y + 2x - 3y = 15 + 4$

$\implies 5x = 19$

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

Put value of x in equation (1) , we get

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

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

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

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

Therefore,

$\ { x = \frac{19}{5} \:Or \: y = \frac{6}{5} }$

Answer 2

x - y = 5 _(i) 2x - 3y = 5 _(ii)

• MULTIPLY (i) by 3

3x - 3y = 15 2x - 3y = 5

• SUBTRACT BOTH

3x - 3y - (2x - 3y) = 15 - 5

x = 10

• PUT x = 10 in (i)

10 - y = 5

y = 5