Final answer:
To solve the system of equations, we can use the method of elimination. Multiply the equations to eliminate the y variable and add the equations together to solve for x. Substitute the value of x back into one of the equations to solve for y. The solution is (x,y) = (5,-4).
Step-by-step explanation:
To solve the system of equations 5x + 4y = 9 and 4x - 5y = 40, we can use the method of substitution or elimination. Let's solve it using the method of elimination.
Multiply the first equation by 5 and the second equation by 4 to eliminate the y variable: (25x + 20y = 45) and (16x - 20y = 160)
Add the two equations together to eliminate the y variable: 41x = 205
Divide both sides by 41 to solve for x: x = 5
Substitute the value of x back into one of the original equations to solve for y: 5(5) + 4y = 9
25 + 4y = 9
4y = -16
y = -4
Therefore, the solution to the system of equations is (x,y) = (5,-4).