To solve the system of equations:
- x/3 - y/2 = 1
- x/2 + y/5 = 36/5
Let's start by solving equation 1 for x:
x/3 - y/2 = 1
Multiply by 6 to eliminate fractions:
2x - 3y = 6
Now, solve equation 2 for x:
x/2 + y/5 = 36/5
Multiply by 2 to eliminate fractions:
x + 2y = 72
Next, let's solve the system of equations. We can use the substitution method. From equation 1:
2x - 3y = 6 2x = 3y + 6 x = (3y + 6) / 2
Substitute this expression for x into equation 2:
(3y + 6) / 2 + 2y = 72 3y + 6 + 4y = 144 7y = 138 y = 138 / 7 y = 18
Now, substitute y = 18 back into the expression we found for x:
x = (3 * 18 + 6) / 2 x = (54 + 6) / 2 x = 60 / 2 x = 30
Therefore, the solution to the system of equations is: x = 30 y = 18
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