Final answer:
To solve the system of equations x + 2y = -14 and -4x - y = 28, we can use the method of elimination by combining the equations. The solution to the system of equations is x = 42 and y = -28.
Step-by-step explanation:
To solve the system of equations x + 2y = -14 and -4x - y = 28, we can use the method of elimination by combining the equations.
To eliminate the y variable, we can multiply the first equation by 4 and the second equation by 2, which gives us:
4(x + 2y) = 4(-14) and 2(-4x - y) = 2(28)
Simplifying these equations, we get:
4x + 8y = -56 and -8x - 2y = 56
Adding these equations together, we eliminate the y variable and get:
-4x + 6y = 0
Now we can solve for x by multiplying this equation by -1/4:
x = (1/4)*(-4x + 6y)
Simplifying further, we get:
x = -1.5y
Substituting this value of x into the first equation, we can solve for y:
-1.5y + 2y = -14
0.5y = -14
y = -28
Now substituting this value of y back into the equation x = -1.5y, we can solve for x:
x = -1.5*(-28)
x = 42
Therefore, the solution to the system of equations is x = 42 and y = -28.