2x+3y=12 x-y=6 solve the following system equations

(6, 0)

Step-by-step explanation:

There are a few different methods to solve system of equations.  For this problem, you can use substitution by solving one of the equations for a variable and then substituting this expression into the other equation to solve for the remaining variable:

x - y = 6, add 'y' to both sides to solve for 'x':  x - y + y = 6 + y or x = 6 + y

Using the expression '6 + y' for the value of 'x' in the second equation:

2x + 3y = 12 or 2(6+y) + 3y = 12 or 12 + 2y + 3y = 12 or 12 + 5y = 12

Subtract 12 from both sides: 12 + 5y - 12 = 12 - 12 or 5y = 0 so y = 0

Now that you know the value of 'y', you can solve for 'x':

x = 6 + 0 or x = 6

Put the values of 'x' and 'y' into an ordered pair: (6,0).