Question

If $3x-2y=24$ and $2x-3y=18$ then find $x+y$ and $x-y$

Answer 1

3x-2y=24 _____ (1)

2x-3y=18 _____ (2)

multiply (1) by 2

6x - 4y = 48

multiply (2) by 3

6x-9y=54

subtracting

6x - 4y = 48

6x - 9y = 54

- + -

___________

5y = -6

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

$3x-2(-\frac{6}{5})=24$

$=3x+\frac{12}{5}=24$

$=3x=24-\frac{12}{5}=\frac{120-12}{5}=\frac{108}{5}$

$\therefore x=\frac{36}{5}$

$x+y=\frac{36-6}{5}=\frac{30}{5}=6$

$x-y=\frac{36+6}{5}=\frac{42}{5}$