Final answer:
The system of equations 7x+5y=22 and 4x-5y=44 is solved using the elimination method. Adding both equations eliminates y, resulting in x=6. Substituting x into one of the equations gives y=-4, so the solution is x=6 and y=-4.
Step-by-step explanation:
To solve the simultaneous equations for the unknowns x and y, we can use the method of addition, also known as the elimination method. The two equations given are 7x+5y=22 and 4x-5y=44.
Step 1: Add the two equations together to eliminate y.
(7x + 5y) + (4x - 5y) = 22 + 44
7x + 4x = 66
11x = 66
x = 6
Step 2: Substitute the value of x into one of the original equations to find y.
4x - 5y = 44
4(6) - 5y = 44
24 - 5y = 44
-5y = 44 - 24
-5y = 20
y = -4
Therefore, the solution to the system of equations is x = 6 and y = -4.