2/3x-1/5y=2, 4/3x+4y=4
To solve this system of equations, you can use either the substitution method or the elimination method. Let's use the elimination method in this case.
Step 1: Multiply the first equation by 15 and the second equation by 5 to clear the fractions:
(15)(2/3x) - (15)(1/5y) = (15)(2)
(5)(4/3x) + (5)(4y) = (5)(4)
Simplifying these equations, we get:
(10/3)x - 3y = 30
(20/3)x + 20y = 20
Step 2: Multiply the first equation by 20 and the second equation by 3 in order to eliminate x when we add the two equations together:
(20)(10/3)x - (20)(3y) = (20)(30)
(3)(20/3)x + (3)(20y) = (3)(20)
Simplifying these equations, we get:
(200/3)x - 60y = 600
20x + 60y = 60
Step 3: Add the two equations together to eliminate y:
(200/3)x - 60y + 20x + 60y = 600 + 60
Simplifying this equation, we get:
(200/3 + 20)x = 660
(200/3 + 60/3)x = 660
(260/3)x = 660
Step 4: Solve for x by multiplying both sides of the equation by 3/260:
x = (660)(3/260)
x = 6
Step 5: Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:
2/3(6) - 1/5y = 2
4 - 1/5y = 2
-1/5y = -2
y = (-2)(-5/1)
y = 10
Therefore, the solution to the system of equations is x = 6 and y = 10.