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Solve the system of equations.
5x+4y=9
4x-5y=40
(x,y)=

1 Answer

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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).

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