Question

Which of the following ordered pairs is a solution of the system? x + 3y = 12 y-x=12

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer is ( -6, 6 )
Step by step
We have two equations
I like to label them first
x + 3y = 12 we will call A
y - x = 12 we will call B

I like to have the equations be in y intercept form to make the math easier
So I will change equation A to
3y = -x + 12
and change B to
y = x + 12

Now we will substitute the value of y of equation B into equation A

3(x + 12) = -x + 12
distribute
3x + 36 = -x + 12
now Isolate x on one side by adding x to both sides
3x + x + 36 = -x + x + 12
Combine like terms
4x + 36 = 12
Now subtract 36 from both sides to isolate x
4x +36 -36 = 12 - 36
Combine terms
4x = -24
Now solve for x by dividing both sides by 4
4/4x = -24/4
x = -6

Now to find y
Substitute your x value into equation B
y = x + 12
y = -6 + 12
y = 6

So your answer is (-6 , 6)

Check your work with equation
x + 3y = 12 from the original question
Substitute x and y values

-6 + 3(6) = 12
-6+18 = 12
12 = 12

Now do the same with the other equation
y - x = 12
6 - (-6) = 12
6 + 6 = 12
12 = 12

Both are Correct, so problem solved