Final answer:
The system of equations -2x - 7y = -37 and x + y = 1 is solved using substitution to find x = -6 and y = 7. The solution is checked and found to be reasonable by substituting these values back into the original equations.
Step-by-step explanation:
To solve the system of equations -2x - 7y = -37 and x + y = 1 by combining the equations, let's use substitution or elimination. Since the second equation is already solved for y in terms of x, we can easily do substitution.
First, we solve the second equation for y:
y = 1 - x
Now we substitute this expression for y into the first equation:
-2x - 7(1 - x) = -37
Simplify the equation and solve for x:
-2x - 7 + 7x = -37
5x - 7 = -37
x = -30 / 5
x = -6
Substitute x = -6 into the equation y = 1 - x to find y:
y = 1 - (-6)
y = 7
The solution to the system of equations is x = -6 and y = 7.
To check the reasonableness of our answer, we substitute x and y into the original equations to see if they are true:
-2(-6) - 7(7) = 12 - 49 = -37 (true)
-6 + 7 = 1 (true)
Both original equations are satisfied by our solution, so our answer is reasonable.