I am really have a tough time trying to solve this problem. I think my first three steps are correct but I am not sure. Could someone please help me? I got lost somewhere on one of these steps. I thonk it was step 3, 4, 5. Thank you.

The two numbers chosen for my solution will be 3 and 6.

Solving the system of equations by the Addition/Subtraction method

Step 1 – Write both equations in the form of ax+ by= c
Equation 1: 4x-y = 3
Equation 2: x+y = 6

Step 2 –Multiply one or both equations by numbers so that the absolute values of the either of the coefficients of the x terms or the y terms are alike, I will multiply my equation by -4.
x + y = 6
-4(x + y) = -4(6)
-4x -4y = -24

Step 3 – Eliminate one of the variables by adding the equations if the signs of the coefficients of the variable are different. Subtract the equations if the signs of the coefficients of the variable are the same.
(4x – y = 3) + (-4x -4y = -24)
-3y = -12 --> y = 3

Step 4 – Plug back into equation 1 to solve for x:
4x – y = 3
4x – (3) = 6
2x = 12 --> x = 6

Step 5

CHECK using equation 2:
x+y = 6+ 3 = 9
So the solution is (6

This looks like a lot of

"Much Ado About Nothing"

If your equations are
4x-y=3 and
x+y = 6 , why not just add them as they are?
5x=9
x=9/5 or 1.8

sub into x+y=6
you can get
y = 4.2

your solution of x=6, y=3 work in your second equation, but not in the first.
So your solution is incorrect.
The error was when you added your equations
4x-y=3
-4x-4y=-24
------------
-5y = -21
y = -21/-5 = 4.2
etc.

x=9/5

y=21/5

solve one equation for x and plug the answer to the other equation and solve it

Btw if you need help with Intersections, use Desmos calculator! It gives you answers for that stuff,

Desmos/graphing

To determine where you went wrong in Step 3, we can review the calculations.

Step 3 involves eliminating one of the variables by adding or subtracting the equations. In your case, the signs of the coefficients of the y variable are the same (-1 and -4), so you should subtract the equations. Let's go through the calculation:

First equation: 4x - y = 3
Second equation (multiplied by -4): -4x - 4y = -24

Now, we subtract the equations:

(4x - y = 3) - (-4x - 4y = -24)

Expanding the subtraction:

4x - y + 4x + 4y = 3 + 24

Combining like terms:

8x + 3y = 27

So, the correct result after eliminating the variable y is 8x + 3y = 27, not -3y = -12 as you had written.

Now, let's continue to Step 4:

Step 4 – Plug back into equation 1 to solve for x:
4x - y = 3
4x - 3 = 6
4x = 9
x = 9/4 or x = 2.25

Finally, Step 5:

To check the solution, substitute the values of x and y into equation 2:

x + y = 6
2.25 + y = 6
y = 6 - 2.25
y = 3.75

So, the correct solution is x = 2.25 and y = 3.75, not x = 6 as you mentioned.

I hope this helps clarify where you went wrong and how to correctly solve the problem.