+112 Consider this system of equations:
\(^2/_3x+\text{ }^3/_5y=12\) (equation A)
\(^5/_2y-3x=6\)(equation B)
The expression that gives the value of x is \(\boxed{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\downarrow}\).
The solution for the system of equations is \(\boxed{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\downarrow}\).
\(\boxed{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\downarrow}\\ \boxed{^{5a}/_3+\text{ }^{2b}/_5\text{ }\text{ }\text{ }\text{ }\text{ }\\\ ^{3a}/_5-\text{ }^{5b}/_2\\ ^{5a}/_2+\text{ }^{3b}/_5\\ ^{5a}/_3-\text{ }^{2b}/_5\\ ^{3a}/_2+\text{ }^b/_5}\) \(\boxed{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\downarrow}\\ \boxed{(^{1118}/_{47},\text{ }^{396}/_{47})\text{ }\text{ }\text{ }\\ (^{33}/_{13},\text{ }^{50}/_{13})\\ (^{99}/_{13},\text{ }^{150}/_{13})\\ (8,12)}\)
+128474 (2/3)x + (3/5)y = 12
-3x + (5/2)y = 6
Mutiply the first equation through by the common denominator of 3 and 5 = 15
Multiply the second equation through by 2
So we have
10x + 9y = 180 multipy through by 6 = 60x + 54y = 1080 (1)
-6x + 5y = 12 multiply through by 10 = -60x + 50y = 120 (2)
Add (1) and (2)
104y = 1200 divide by 104
y = 1200/104 = 600/52 = 150 / 13
Obviously, only one answer has a "y" answer that = 150/13.....so that must be the correct one
