Question

Solve the system of equations using elimination: -5x + 2y = 1 and -4x - y = 19. What is the solution?

a) (-2, 3)
b) (5, -9)
c) (3, -4)
d) (1, -2)

Answer 1

Using elimination, the equations -5x + 2y = 1 and -4x - y = 19 solve to x = -3 and y = -7, which does not match any of the given options.

Step-by-step explanation:

To solve the system of equations using elimination for -5x + 2y = 1 and -4x - y = 19, follow these steps:

1. Multiply the second equation by 2 to get -8x - 2y = 38.
2. Add this equation to the first equation to eliminate y: (-5x + 2y) + (-8x - 2y) = 1 + 38, simplifying to -13x = 39.
3. Divide both sides by -13 to find x: x = 39 / -13, x = -3.
4. Substitute x = -3 into the first equation to find y: -5(-3) + 2y = 1, which simplifies to 15 + 2y = 1.
5. Subtract 15 from both sides to solve for y: 2y = 1 - 15, 2y = -14.
6. Divide both sides by 2: y = -14 / 2, y = -7.

The solution of the system of equations is (-3, -7), which is not present in the given options, implying there might have been an error in either the provided equations or the answer choices.