which method would be the simplest way to solve the system?

Question

y= -3x
3x+2y=6

Answer 1

To solve the system of equations by the simplest method, we would look for a direct substitution since one of the equations is already solved for y in terms of x. The system of equations given is:

1) y = -3x
2) 3x + 2y = 6

Using equation 1), we can directly substitute -3x for y in equation 2). Doing the substitution we get:

3x + 2(-3x) = 6
3x - 6x = 6
-3x = 6
x = -2

Now that we have found the value of x, we can substitute it back into equation 1) to find the value of y:

y = -3(-2)
y = 6

Therefore, the solution to the system of equations is x = -2 and y = 6. This substitution method is generally the simplest way to solve when one of the equations is already solved for one of the variables. In this case, it allowed us to solve the system of equations very efficiently.