Question

Solve the system of equations below:

−3x+6y=−49
5x+7y=0
A) (-2, 1)
B) (-2, -7)
C) (-7, -2)
D) (1, -2)

Answer 1

The correct solution to the system of equations -3x + 6y = -49 and 5x + 7y = 0 is (7, -5) using the elimination method, but this solution does not match any of the provided options.

Step-by-step explanation:

To solve the system of equations -3x + 6y = -49 and 5x + 7y = 0, we can use either substitution or elimination method. Let's opt for the elimination method here to make the calculations straightforward:

1. Multiply the first equation by 5 and the second equation by 3. This will make the coefficients of x equal (but opposite in sign), enabling us to eliminate x.
   -3x * 5 → -15x + 30y = -245
   5x * 3 → 15x + 21y = 0
2. Add the two new equations to eliminate x: (-15x + 30y) + (15x + 21y) = -245 + 0, which simplifies to 51y = -245.
3. Divide both sides by 51 to find the value of y: y = -245 / 51, which simplifies to y = -5.
4. Substitute y = -5 into one of the original equations (let's use the second one) to find x: 5x + 7(-5) = 0. This simplifies to 5x - 35 = 0.
5. Add 35 to both sides and divide by 5 to find x: 5x = 35, so x = 35 / 5, which simplifies to x = 7.

The solution to the system is (7, -5), which is not listed among the options A) (-2, 1), B) (-2, -7), C) (-7, -2), D) (1, -2). There seems to be an error either in the provided options or in the system of equations.