Final answer:
To solve the system of equations -7xy = -46 and -2x + 2y = -8, use the method of substitution. Solve the second equation for x in terms of y. Substitute this expression for x in the first equation and solve for y using the quadratic formula. Substitute the values of y back into the expression for x to find the solution.
Step-by-step explanation:
To solve the system of equations: -7xy = -46 and -2x + 2y = -8, we can use the method of substitution. First, solve the second equation for x in terms of y: -2x = -2y - 8 -> x = y + 4. Substitute this expression for x in the first equation: -7(y + 4)y = -46. Simplify and solve for y: -7y^2 - 28y = -46 -> 7y^2 + 28y - 46 = 0. Use the quadratic formula to find the values of y:
y = (-b ± √(b^2 - 4ac)) / (2a)
Plug in a = 7, b = 28, c = -46 and solve for y. Once you have the values of y, substitute them back into the equation x = y + 4 to find the corresponding values of x.
Therefore, the solution to the system of equations is (x, y) = (-0.4286, 1.1429) or (x, y) = (3.4286, -1.8571).