Find the ordered pair solution to the following system of equations (Use any method?

Question

Find the ordered pair solution to the following system of equations (Use any method):

3x – y = 2

y = 4x – 3

Answer 1

3x - y = 2
y = 4x - 3

First things first, let's move all variables to the left hand side, in the order of x and y variables.

3x - y = 2
-4x + y = -3

Let's solve this by elimination. Add the two equations together, to get

-x = -1, which means x = 1.

Since x = 1, we can substitute x = 1 into any equation. Let's substitute it into -4x + y = -3.
-4(1) + y = -3
-4 + y = -3
y = 1

So the solution would be x = 3, y = 1, or (3,1) for the ordered pair.

Answer 2

I would tend to disagree with the answer of (3,7) as it doesn't check in both equations if you plug it back in. I did it like this:

3x - y = 2
y = 4x - 3

Since you're working with a system, you want to get two things that look the same so you can subtract them.

Take y = 4x - 3 and add 3 to both sides.

y + 3 = 4x

Now subtract y from both sides.

3 = 4x - y

Flip it around. . .

4x - y = 3

Now it looks just like 3x - y = 2.

Put one on top of the other like this.

3x - y = 2
4x - y = 3

The whole idea is to isolate one variable so you can find out what it is, so change one of the equations so that one of the variables drops out. This one isn't too hard to do that with, just multiply one by -1.

-3x + y = -2
4x - y = 3

If you add the two equations together, the "y"s cancel out and you get

x = 1

Now that you have x, just plug it into either one of the originals to find y.

3(1) - y = 2
3 - y = 2

Subtract 3 from both sides.

-y = -1

So y = 1. You're ordered pair is (1,1). If you go back and check, just plug 1 in for x in both equations and make sure you get 1 for y in both cases.

3(1) - y = 2
3 - y = 2
-y = -1
y = 1

y = 4(1) - 3
y = 4 - 3
y = 1

Everything checks out, so you're ordered pair is still (1,1)

Answer 3

Number 1:
-First, you need to solve the equation for y.
3x-y=2
-y=-3x+2
y=3x-2
-Second, you plug any number into x, lets use 3 as our example.
y=3(3)-2
y=9-2
y=7
-Last, write your ordered pair solution. Ordered pair solutions are written as (x,y). In our example, we gave x the value of 3 which gave y the value of 7. Your ordered pair solution is (3,7).


These types of problems can have any answeres though, because you can give x any value. Your second question can be solved the same way, just starting at step two.

Answer 4

Substitute the y=4x-3 into the 3x-y=2 equation:
3x-(4x-3)=2
3x-4x+3=2
-x+3=2
-x=-1
x=1

y=4(1)-3
y=4-3
y=1

The solution set is (1,1)

Check:
3(1)-1=2
3-1=2
2=2

1=4(1)-3
1=4-3
1=1

Answer 5

1,1
3*1-1=2
3-1=2
1=4*1-3
1=4-3