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 ?
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)
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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