Final answer:
To solve the system of equations 4x + 7y = -23 and 8x + 5y = -1, we can use the method of substitution. The solution is x = -18, y = 7.
Step-by-step explanation:
This question involves solving a system of linear equations. We are given two equations:
Equation 1: 4x + 7y = -23
Equation 2: 8x + 5y = -1
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
From Equation 1, isolate for x: 4x = -23 - 7y. Simplify: x = (-23 - 7y) / 4.
Substitute this value of x into Equation 2: 8((-23 - 7y) / 4) + 5y = -1. Simplify and solve for y: -46 - 14y + 20y = -4. Combine like terms: 6y = 42. Divide both sides by 6: y = 7.
Substitute y = 7 back into Equation 1 to solve for x: 4x + 7(7) = -23. Simplify and solve for x: 4x + 49 = -23. Subtract 49 from both sides: 4x = -72. Divide both sides by 4: x = -18.
Therefore, the solution to the system of equations is x = -18, y = 7.