Respuesta :
To solve the system of linear equations 6x + 2y = 16 and -3x - y = -8, we can use the method of substitution or elimination. Here, I'll demonstrate the method of elimination:
Given equations:
6x + 2y = 16 (1)
-3x - y = -8 (2)
To eliminate one of the variables, let's multiply equation (2) by 2 to make the coefficient of y equal to the coefficient of y in equation (1):
-6x - 2y = -16
Now, we'll add equation (1) and the modified equation (2):
6x + 2y = 16
-6x - 2y = -16
Adding the equations, we get:
0 = 0
This result indicates that the two equations represent the same line, and they are dependent. In other words, there are infinitely many solutions. Any point on the line represented by the equation 6x + 2y = 16 and -3x - y = -8 satisfies both equations.
So, the solution set for the system of equations is all points on the line represented by either equation.
