Final answer:
To solve the system of equations by elimination, we need to eliminate one variable by adding or subtracting the equations. However, in this case, the resulting equation is not possible, which means there is no solution to the system of equations.
Step-by-step explanation:
To solve the system of equations by elimination, we need to eliminate one variable by adding or subtracting the equations. Let's start by eliminating the y variable.
Given equations:
-4 + 2y = -38
4x + y = 11
By multiplying the second equation by 2, we can create a cancellation:
-4 + 2y = -38
8x + 2y = 22
Now, add the two equations:
8x - 4 + 2y + 2y = 22 - 38
8x - 2 + 4y = -16
Simplify:
8x + 4y = -16
This leaves us with one equation in two variables. To solve for x, we need another equation. Let's go back to the given equations:
-4 + 2y = -38
4x + y = 11
By multiplying the first equation by 4, we can create a cancellation:
-16 + 8y = -152
4x + y = 11
Now, add the two equations:
4x - 16 + y + y = 11 - 152
4x + 2y = -141
Simplify:
4x + 2y = -141
Now, we have a system of two equations with the same coefficients:
8x + 4y = -16
4x + 2y = -141
From here, we can solve the system of equations. Multiplying the second equation by 2:
8x + 4y = -16
8x + 4y = -282
Now, subtract the equations:
8x + 4y - (8x + 4y) = -16 - (-282)
Simplify:
0 = -16 + 282
0 = 266
Since this equation is not possible, there is no solution to the system of equations by elimination.