Question

2x - 1y = 6 -3y = -6x + 18 please explain how you got your answer thank you :)

Answer 1

Answer: {x,y}={6,21}

Step-by-step explanation:

// Solve equation [2] for the variable  x

  [2]    3x = 18

  [2]    x = 6

// Plug this in for variable  x  in equation [1]

  [1]    2•(6) - y = -9

  [1]     - y = -21

// Solve equation [1] for the variable  y

  [1]    y = 21

// By now we know this much :

   x = 6

   y = 21

We are done

Answer 2

Answer:

y = 2x -6. A dependent system, so all numbers on this line.

Step-by-step explanation:

2x - y = 6

-3y = -6x + 18

In order to solve a system of equations, you want to get isolate y. One equation already has done that for us, so that makes it easier.

2x - y = 6

In order to isolate y in this equation, you must simply subtract 2x from both sides, which would give us:

-y = -2x + 6

Now, you can't leave y negative. Normally you'd divide the y by its variable, but this one doesn't have a variable. so you must divide both sides by -1.

$\frac{-y}{-1} =\frac{-2x+6}{-1}$

We divide both sides because what you do to one side you must do to the other. This leaves us with the equation:

y = 2x - 6

Now, for the other equation. It's simple since y is already isolated.

-3y = -6x + 18

Once again we will be dividing both sides, but this time it's by -3.

$\frac{-3y}{-3} =\frac{-6x+18}{-3}$

We are dividing by -3 instead of -1 because y in this equation has a variable of -3. This would give us:

y = 2x - 6

Now, normally in order to get the answer, you must graph both of these equations, but since these equations ended up being the same, the answer is every number that appears on the line. This is called a dependent system.