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what's the ordered pair of y=2X-5 and 4X-Y=7 ?

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5 Answers

If y=2x-5 is equation (1) and 4x-y=7 is equation (2), then substitute equation (1) in equation (2):

         4x - (2x - 5) = 7

         4x - 2x + 5 = 7

         2x = 7-5

         2x = 2

         x = 1

 

Now substitute the value of x in equation (1) to find the value of y:

        y = 2 (1) - 5

        y = 2 - 5

        y = -3

 

Therefore the ordered pair is (1, -3).

Problem:  How do you find the ordered pair for these two equations?

(1)  y = 2x - 5

(2)  4x - y = 7

The biggest difficulty is that you cannot solve one equation with two variables, so you have to use a trick to solve this problem.  Here it is:

You can solve this problem by substitution. Notice that the first equation tells you that y is equal to 2x - 5.  That means that you can substitute 2x - 5 in place of y in the second equation!  Aha!!

It looks like this:

  4x -      y     = 7

  4x - (2x - 5) = 7  Now solve for x!  (Don't forget that the negative sign in front of the parenthesis means you have to multiply both numbers by negative one.)

 4x - 2x + 5 = 7

        2x + 5 = 7

             - 5    -5

         2x      =  2

          2           2

            x   =   1   Good trick, huh!

Now that you know the value of x, substitute the number 1 for x in the first equation, like this:

      y = 2 x - 5

      y = 2(1) - 5

      y = 2 - 5

      y = -3

So, to answer your question, since x = 1 and y = -3, the ordered pair for the two linear equations is (1, -3)  This is the point where these two lines intersect.

y=2X-5 and 4X-Y=7

Putting the value of Y in 2nd equation:

4x-2x+5=7

2x=7-5

2x=2

OR,x=2/2=1

 

putting the value of x in equation 1:

y=2x-5

y=2*1-5

y=2-5

y=-3

 

y = 2x - 5 ............ (1)
4x - y = 7 ............ (2)
 
            y from (1)
            ↓
4x - (2x - 5) = 7 ----> 4x + (-1)(2x - 5) = 7
4x - 2x + 5 = 7 ------> 2x + 5 = 7
                                      - 5   - 5
                                  2x      = 2 ------> 2x/2 = 2/2 ------> x = 1
Now in (1), let's replace x by 1 ---------> y = 2 · 1 - 5 = -3
The answer is pair of numbers 1 and -3: (1,-3)
~~~~~~~~~~~~
Check:
(1) ...... -3 = 2 · 1 - 5      (2) ....... 4 · 1 - (-3) = 7 
            -3 = -3                               4   +  3   = 7
                                                                7 = 7

4x  - y = 7

-2x + y = -5             (rearranging the first equation)

---------------------------------------------

2x        = 2             (adding the two equations)

x = 1

y = 2(1)-5 = -3      (substituting the value for x in the first equation)

 

x=1, y=-3