Explanation:
Consider this equality as two separate equations:
7x+10y=36y
36y=-2x+9
Now, we have a system of equations. Let's use substitution method to solve. Substitution method involves solving one equation for a variable--then plugging that result into the other equation.
Let's solve 36y=-2x+9 for x:
36y=-2x+9 (Given)
36y-9=(-2x+9)-9 (Subtraction Property of Equality)
36y-9=-2x (Simplification)
(36y-9)/(-2)=(-2x)/(-2) (Division Property of Equality)
-18y+(9/2)=x (Simplification)
Now, we get to substitute -18y+(9/2) for x into the other equation:
7x+10y=36y (Given)
7(-18y+(9/2))+10y=36y (Substitution)
-126y+(63/2)+10y=36y (Distributive Property)
-126y+10y+(63/2)=36y (Commutative Property of Addition)
-116y+(63/2)=36y (Simplification)
(-116y+(63/2))+116y=36y+116y (Addition Property of Equality)
63/2=152y
(63/2)/152=(152y)/152 (Division Property of Equality)
63/304=y (Simplification)
Yay, after all that hard work, we've finally found one of our variables! :) Now, we've just got to substitute our y value into one of the original equations. That way, we can solve for x.
Let's substitute into 36y=-2x+9:
36y=-2x+9 (Given)
36(63/304)=-2x+9 (Substitution)
(2268/304)=-2x+9 (Simplification)
(2268/304)-9=(-2x+9)-9 (Subtraction Property of Equality)
(2268/304)-9=-2x (Simplification)
(2268/304)-9(304/304)=-2x (Common Denominators on Left Side)
(2268/304)-(2736/304)=-2x (Simplification)
(-468/304)=-2x (Simplification)
(-468/304)/(-2)=(-2x)/(-2) (Division Property of Equality)
234/304=x (Simplification)
117/152=x (Simplification)
Our final answers are x=117/152 and y=63/304.
Answer: x=117/152 and y=63/304