Final answer:
None of the provided options (A, B, C, D) match the solution obtained from the calculations for the system of equations: 5x + 4y = -54 and -3x + 2y = 5.
Step-by-step explanation:
To find the solution to the system of equations given by:
5x + 4y = -54
-3x + 2y = 5
We can use the method of substitution or elimination. In this case, we'll use the elimination method. We want to eliminate one of the variables by making the coefficients of x or y the same in both equations. We notice that the coefficients of y in both equations are related by a factor of 2 (4 and 2), so we can multiply the second equation by 2 to make the coefficients match:
- First, multiply the second equation by 2:
-3x + 2y = 5 becomes -6x + 4y = 10 - Add this equation to the first equation:
5x - 6x + 4y + 4y = -54 + 10
-x + 8y = -44 - Solve for y:
8y = -44 + x
y = -44/8 + x/8
y = -5.5 + 0.125x - Substitute y in one of the original equations (use the simpler one, -3x + 2y = 5):
-3x + 2(-5.5 + 0.125x) = 5
-3x - 11 + 0.25x = 5
-2.75x = 16
x = 16 / -2.75
x = -5.8181... (This does not match any of the provided options) - Solve for y using x = -5.8181...:
5(-5.8181...) + 4y = -54
-29.0905 + 4y = -54
4y = -54 + 29.0905
4y = -24.9095
y = -24.9095 / 4
y = -6.227375 (This does not match any of the provided options)
It appears none of the provided options match the solution obtained from the calculations. There might be a mistake in the original equations, the answer choices provided, or in the calculation process. To check this further, we could substitute the options into the original equations to confirm.