Question

solve 3ₓ+5y=10 : 5x+3y=6 find the value of x+y.

Answer 1

3x + 5y = 10 ------(I)

5x + 3y = 6 ------(II)

Multiplying equation-----(I) with 5 and-----(II) with 3

15x + 25y = 50 ------(III)

15x + 9y = 18 -------(IV)

Subtracting

equation ------(IV) from ------(III)

_____________________

→ 15x + 25y - ( 15x + 9y ) = 50 - 18

→ 15x + 25y - 15x - 9y = 50 - 18

→ 16y = 32

${y\:=\:\frac{32}{16}}$

$\boxed{y\:=\:2}$

_____________________

substituting y = 2 in equation ------(IV)

15x + 9y = 18 -------(IV)

→ 15x + 9y = 18

→ 15x + 9(2) = 18

→ 15x + 18 = 18

→ 15x = 18 - 18

→ 15x = 0

${x\:=\:\frac{0}{15}}$

$\boxed{x\:=\:0}$

$\large\boxed{\color{cyan}{(x,y)\:=\:(0,2)}}$