Question

Pleas help I don't understand this on. Solve the system by using elimination or elimination with multiplication: -5X = -6 - Y and -3 = 2X - y. Thanks

Answer 1

To use elimination to solve a system of equation means that you will add the equations and one variable will add up to zero.
For example, look at this very simple system of equations:
x + y = 14
x - y = 2
Notice that if you add the equations, the y variable will add up to zero since one equation has y and the other one has -y.
Adding the equations would give you:
2x = 16
Now you can solve for x,
x = 8.
Then you substitute x into one o the original equations to find y.
x + y = 14
8 + y = 14
y = 6
The solution is x = 8, y = 6
This was all an example, so you understand how the method works.

Answer 2

Now let's look at your problem.
The first step is to write the two equations, one above the other.
The two equations must be written in the same form.
The usual way to do it is to write all the terms with variables on the left side and the numbers on the right side.

Answer 3

Here are your equations the way they were given:
-5x = -6 - y
-3 = 2x - y
Let's work on them so we have all variables on the left side and plain numbers on the right side.
Let's start with the first equation. We add y to both sides to have al;l variables ont he left side:
-5x + y = -6
Now for the second equation, we see that the variables are on the right side and the number is on the left side, so we just switch sides.
2x - y = -3
Now we write the new versions of our equations, one above the other.
-5x + y = -6
2x - y = -3

Answer 4

Now we are ready to use elimination.

Answer 5

BTW, do you understand it so far?

Answer 6

Thanks for the help but I really don't get it. Here is what I did: -6 - Y = -5X and 2X - Y = -3; the answer I got was 4X and -8. Please tell me if I am on the right track before I do any more?

Answer 7

No, I don't understand how you got there.

Answer 8

Now you take the two new equations from your problem and look at them.
Notice you have y and -y. y and -y add up to zero, so y will cancel out. That's what we want.
Let's add the equations:
-3x = -9
Divide both sides by -3 to get:
x = 3
Now we substitute x = 3 into our original first equation to get:
-5x = -6 - y
-5(3) = -6 - y
-15 = -6 - y
-9 = -y
y = 9
Solution: x = 3 and y = 9

Answer 9

That's how you use elimination.
Go over it a few times and read the explanations.

Answer 10

thank you mathstudent55. By breaking it down help me understand it better.

Answer 11

yeah he or she did good explaing that

Answer 12

You're welcome.