I am taking math 116 , I am to find the solution to the problem 9x-3y=-68 and -2x+y=18 and to give an ordered pair. Now, that you have it where you take 9x from both sides, or is it 3y? My question is when you just have y do you count that as one(y) , I try to work the problem and every time I do the substitution for both sides I come up with several different answers. I have worked on this most of the afternoon, and just can't figure out where I am going wrong. I add , sub. and divided on my own then I recheck it with a calulator. I still come up wrong. One answer says 272, 204, 9=one of the points, 4 =equals another, Please help me, I am so confused over just what the steps are and if I am chooing the right variable to multiply or do away with.

Question

I am taking math 116 , I am to find the solution to the problem 9x-3y=-68 and -2x+y=18 and to give an ordered pair. Now, that you have it where you take 9x from both sides, or is it 3y? My question is when you just have y do you count that as one(y) , I try to work the problem and every time I do the substitution for both sides I come up with several different answers. I have worked on this most of the afternoon, and just can't figure out where I am going wrong. I add , sub. and divided on my own then I recheck it with a calulator. I still come up wrong. One answer says 272, 204, 9=one of the points, 4 =equals another, Please help me, I am so confused over just what the steps are and if I am chooing the right variable to multiply or do away with.

Answer 1

In problems like this, you look for a variable which you can eliminate by adding the two equations multiplied by appropriate factors.

For the given problem, if you multiply the second equation and add the whole equation to the first, the "y" terms will cancel out leaving you with a single equation in x, which you can solve by transposition and finally division by the coefficient of x.
Once you have obtained the value of x, you will substitute this value to any of the two equations to result in an equation in y. Solve this equation for y and substitute the values of x and y back into the original equations as a check.
If you want to post your calculations and answers for checking or comments, you are welcome to do so.

Answer 2

I understand that you're facing difficulties in solving the system of equations 9x - 3y = -68 and -2x + y = 18. Let's break down the steps to solve this system using the method of substitution:

Step 1: Choose one of the equations to solve for a variable in terms of the other variable. In this case, let's solve the second equation for y in terms of x:
-2x + y = 18 ---> y = 2x + 18

Step 2: Substitute the expression for y (2x + 18) from the second equation into the first equation.
9x - 3(2x + 18) = -68

Step 3: Simplify and solve the resulting equation for x. Let's go through the steps:
9x - 6x - 54 = -68
3x - 54 = -68
3x = -68 + 54
3x = -14
x = -14 / 3

So, x = -14/3.

Step 4: Substitute the value of x (-14/3) into one of the original equations to find the corresponding value of y. Let's use the second equation:
-2(-14/3) + y = 18
28/3 + y = 18
y = 18 - 28/3
y = 54/3 - 28/3
y = 26/3

So, y = 26/3.

Step 5: Write the solution as an ordered pair (x, y). Plugging in the values we found, we have:
(x, y) = (-14/3, 26/3)

Therefore, the solution to the system of equations is (-14/3, 26/3).

It's essential to double-check your calculations and steps to avoid errors. If you're still obtaining different answers, please review the steps and calculations to see if any mistakes were made.