Question 160159
method of comparison works on the principal if a = b and b = c, then a = c.
that's what i understand from what i read.
----
in your equations you have
3*x + 2*y = 7, and
6*x - 5*y = 8
----
solving for x in first equation gets x = (7-(2*y))/3
solving for x in the second equation gets x = (8+(5*y))/6
since (7-(2*6))/3 = x and (8+(5*y))/6 = x, then they must equal to each other, so
(7-(2*y))/3 = (8+(5*y))/6
multiplying both sides by 6 to remove denominators gets
6*(7-(2*y))/3 = 6*(8+(5*y))/6 becomes
2*(7-(2*y)) = (8+(5*y)) becomes
14 - 4*y = 8 + 5*y
adding 4*y to both sides of the equation and subtracting 8 from both sides of the equation gets
14 - 8 = 5*y + 4*y becomes
6 = 9*y becomes
y = 6/9
-----
now that you have y, you substitute in one of the equations to get x.
use the first equation
-----
3*x + 2*y = 7 becomes
3*x + 2*(6/9) = 7
multiply both sides of equation by 9 to remove denominator.
(3*9*x) + (2*6*9)/9 = 7*9
27*x + 12 = 63
27*x = 51
x = 51/27 = 17/9
-----
your answer looks like
x = 17/9
y = 6/9
-----
substituting in first equation gets
3*x + 2*y = 7
3*(17/9) + 2*(6/9) = 7
multiplying both sides of equation by 9 gets
3*17 + 2*6 = 63
51 + 12 = 63
63 = 63
first equation is good.
-----
substituting in second equation gets
6*x - 5*y = 8
6*(17/9) - 5*(6/9) = 8
multiplying both sides of equation by 9 gets
6*17 - 5*6 = 8*9
102 - 30 = 72
72 = 72
second equation is good.
-----