[cooper11]

x + 9y = 7 (1)
x = 3 - 9y (2)

What is the solution of the system?
Type an ordered pair. Type N if there is no solution.

Thank you!
Cooper

[Perito]

x + 9y = 7 (1)
x = 3 - 9y (2)

(1)
(2)

1. Move the 9y in equation 1 to the right-hand side.
2. Subtract the two equations -- subtract the left sides; subtract the right sides.

[cooper11]

(1)
(2)

1. Move the 9y in equation 1 to the right-hand side.
2. Add the two equations -- add the left sides; add the right sides.
3. You will end up with a single equation in one variable (x) that you should be able to solve easily.
4. Plug the value of x that you obtained in #3 into either of the equations; solve for y.
5. Validate by plugging the value of x in the other equation and again solve for y.
6. Write the x and the y you obtained in an ordered pair: (x,y)

I am not sure what I am doing wrong but I am not coming up with a solution? Help!

Thanks!

[Perito]

I should have said "subtract" instead of "add" in #2. (I probably also should have looked at it a bit closer).

subtract 9y from both sides

(Equation 1)

(Equation 2)

Look carefully at the equations. Both have an x on the left; both have -9y on the right. You could rearrange them like this:





That's not possible if the two equations are to have a solution. Subtract the two equations:

. "Huh?". This is obviously not possible. Therefore, the equations have no solution (they're equations of parallel lines). In order to have a solution, the lines have to intersect.)

Type "N"

[Unknown008]

Also, to show you why there is no solution, you can fraw the two graphs. To do this, put them in the form

That brings the equations to and

The solutions are where the two lines meet. If they do not, there is no solution. Here, you'll see that their gradient are the same, and the lines are parallel. Do parallel lines ever meet? The answer is no, and therefore, there are no solutions.

[pready]

There is an easier way to solve for these 2 equations:

1. X+9y=7
2.X=3-9y

On number 2 you already know what X equals so insert this answer into X for #1.
(3-9Y)+9Y=7
3-9Y+9Y=7
-9y+9Y cancel each other out so you are left with 3 = 7, which is not true therefore there is no solution.

[Unknown008]

You cannot tell which method is easier. Some people find it easier through graphs, others by substitution, others by elimination. All these are good, provided you get the correct conclusion.