Answer:
To solve the system of equations:
2/3x + 3/5 y = 12 --- equation (1)
5/2y - 3x = 6 --- equation (2)
We can use the method of substitution or elimination. Here, we will use the elimination method to eliminate one variable and solve for the other.
Multiplying equation (1) by 5 and equation (2) by 3, we get:
10/3x + 9/5y = 60 --- equation (3) obtained from (1) by multiplying both sides by 5
15/2y - 9x = 18 --- equation (4) obtained from (2) by multiplying both sides by 3
Now, we can eliminate y by multiplying equation (3) by 10/9 and adding it to equation (4):
(10/3x + 9/5y) x 10/9 + (15/2y - 9x) = 0
Simplifying this equation, we get:
20x/9 - 27x/5 = -100/3
Multiplying both sides by 45, we get:
20x(5) - 27x(9) = -1500
Simplifying and solving for x, we get:
-65x = -1500
x = 23.08 (rounded to two decimal places)
Substituting x = 23.08 into equation (1), we can solve for y:
2/3(23.08) + 3/5 y = 12
15.39 + 0.6y = 12
0.6y = -3.39
y = -5.65 (rounded to two decimal places)
Therefore, the solution to the system of equations is x = 23.08 and y = -5.65.
So, the solution to the system of equations is (23.08, -5.65).
Hope this helps.