Final answer:
To solve the system of equations -x-7y=-41 and x-6y=-37, we can use the method of elimination. Multiplying the first equation by 6 and the second equation by -7, we eliminate y from the equations. The solution is x = -505/13 and y = -376/78.
Step-by-step explanation:
To solve the system of equations -x-7y=-41 and x-6y=-37, we can use the method of elimination. We want to eliminate one variable, either x or y, from the equations by multiplying one or both equations by appropriate amounts so that the coefficients of x or y will be equal in magnitude but opposite in sign.
Multiplying the first equation by 6 and the second equation by -7 gives us 6(-x-7y)=-6(-41) and -7(x-6y)=-7(-37). Simplifying, we get -6x-42y=246 and -7x+42y=259. Adding both equations eliminates y, leaving us with -13x=505. Solving for x, we find x = -505/13.
Substituting the value of x back into one of the original equations, x-6y=-37, we can solve for y. Plugging in x = -505/13, we have -505/13-6y=-37. Simplifying and solving for y, we get y = -376/78.