if the equations are

y=2x-5

and

4x-y=7 ,

what is the ordered pair ?

if the equations are

y=2x-5

and

4x-y=7 ,

what is the ordered pair ?

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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

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**