Final answer:
To solve the system of equations using elimination, multiply the first equation by 20 and the second equation by 15 to eliminate the denominators. Add the equations together to eliminate the y terms and solve for x. Substitute the value of x back into one of the original equations to solve for y.
Step-by-step explanation:
To solve the system of equations using elimination, we can multiply the first equation by 20 to get rid of the denominators. This gives us 4x - (20/3)y = 32/15. Then we can multiply the second equation by 15 to get rid of the denominators. This gives us 7x + (15/4)y = 15/4. Now we can add the two equations together to eliminate the y terms. This gives us (4x - (20/3)y) + (7x + (15/4)y) = (32/15) + (15/4), which simplifies to 11x = 67/4. Solving for x, we get x = (67/4) / 11.
Substituting this value of x back into one of the original equations, we can solve for y. Let's use the first equation. Substituting x = (67/4) / 11 into (x/5) - (y/3) = 8/15, we get ((67/4) / 11 / 5) - (y/3) = 8/15. Solving for y, we get y = (5/3) * (67/4) / 11 - 8/15.