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2 answers:
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Answer:
x=-32/29
Step-by-step explanation:
3x+4y=36 Equation 1
-5x+3y=35 Equation 2
Multiplying equation 1 with 3 (value before y in equation 2) and equation 2 with 4 (value before y in equation 1) we obtain equations 3 and 4 as follows
9x+12=108 equation 3
-20x+12y=140 equation 4
Subtracting equation 3 from equation 4 we obtain
-29x=32
x=-32/29
To find the value of y, we substitute the value of x into equation 2 as initially given in the equation
-5(-32/29)=35-3y
-5(-32/29)-35=-3y
Brief review of proportionality relationships:
When two quantities
are 
proportional, that means any change in 
manifests a 
change (think "in the same direction") in 
.
Silly example: "The more I eat, the fatter I get." Here the amount one eats is directly proportional to one's body weight.
This change isn't always one-for-one, so we introduce a constant
to account for any scaling that occurs on either variables behalf. In general, though, we can write a directly proportional relationship as 
.
Now, when are 
proportional, then a change in manifests a change in in the 
(opposite) direction.
Silly example: "The more I eat, the less thin I get."
This time we write the relation as
.
To get back to your problem: To say that the rate of change of
is inversely proportional to 
is to say that there is some constant such that
This is a separable ODE:
When two quantities
Silly example: "The more I eat, the fatter I get." Here the amount one eats is directly proportional to one's body weight.
This change isn't always one-for-one, so we introduce a constant
Now, when
Silly example: "The more I eat, the less thin I get."
This time we write the relation as
To get back to your problem: To say that the rate of change of
This is a separable ODE: