Final answer:
The solution to the system of equations 9x + 5y = 28 and 5x + 9y = 56 is found using the elimination method. By multiplying both equations to match the y coefficients and then subtracting them, we find y = 6.5. Substituting this back into one of the original equations yields x = -0.5.
Step-by-step explanation:
To find the solution set for the system of equations 9x + 5y = 28 and 5x + 9y = 56, we can use the method of substitution or elimination. Let's use the elimination method here. First, we'll multiply the first equation by 5 and the second equation by 9 to make the coefficients of y match:
(5)(9x + 5y) = (5)(28)
(9)(5x + 9y) = (9)(56)
This gives us:
45x + 25y = 140
45x + 81y = 504
Now, we'll subtract the second equation from the first one to eliminate x:
(45x + 25y) - (45x + 81y) = 140 - 504
This simplifies down to:
-56y = -364
Then, solving for y:
y = -364 / -56
y = 6.5
Substitute y = 6.5 back into one of the original equations to solve for x. For instance, using the first original equation:
9x + 5(6.5) = 28
9x + 32.5 = 28
9x = -4.5
x = -4.5 / 9
x = -0.5
Therefore, the solution set is x = -0.5, y = 6.5.