Final answer:
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:
- 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 - Add the two new equations to eliminate x: (-15x + 30y) + (15x + 21y) = -245 + 0, which simplifies to 51y = -245.
- Divide both sides by 51 to find the value of y: y = -245 / 51, which simplifies to y = -5.
- 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.
- 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.