Question

Solve for x and y:

$6(ax+by)=3a+2b,6(bx-ay)=3b-2a.$

Answer 1

6(ax + by)=3a+2b =>> 6ax+6by-3a-2b=0
6(bx - ay)=3b-2a =>> 6bx-6ay-3b+2a=0
By Rule
2 3 1 2
6b -3a-2b 6a 6b
-6a -3b+2a 6b -6a
Now by cross multiplication method
x _​= y ₌ 1
(6b)(-3b+2a) - (-(6a)(-3a-2b) ) (6b)(-3a-2b) - ( (6a)(-3b + 2a) ) (6a)(-6a) - (6b)(6b)
x _​= y ₌ 1
(-18b² + 12ab - 18a² - 12ab) ( -18ab-12b² +18ab - 12a² ) -36a² -36b²
x _​= y ₌ 1
(-18b² - 18a² ) (-12b² - 12a² ) -36(a² +b²)
x _​= y ₌ 1
(-18(b²+a²) ) (-12(b²+a²⁾ ) -36(b²+a²)
NOW WE HAVE
x ₌ 1
(-18(b²+a²) ) ​-36(b²+a²)
x=​-18(b²+a²)
​​-36(b²+a²)
x=1
2
ALSO y=-12(b²+a²⁾ / -36(b²+a²)
y=1/3