Question

Solve the system of equations minus, 2, x, minus, 7, y, equals, minus, 37−2x−7y=−37 and x, plus, y, equals, 1x+y=1 by combining the equations.

Answer 1

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.