4x+y=8 x+y=5

Question

System if equations

Answer 1

There are several ways to solve a system of equations:  the graphing method, the substitution method, and the elimination method.  Have you learned these?

 

For this one let's use the substitution method.

 

First, solve the second equation for y:

 

   x   +   y   =   5

  -x                  -x             subtract x from both sides

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             y   =   -x  +  5

 

Next, substitute (-x + 5) into the first equation for y.

 

  4x   +        y         =   8

 

  4x   +  (-x  +  5)   =   8        substitute

 

        3x     +     5    =   8        simplify by combining like terms

                     -  5       - 5        subtract 5 from each side

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        3x                   =  3

 

       3x/3                 =  3/3     divide both sides by 3

 

         x                    =   1

 

Now you know that x=1.  Remember that you know that x + y = 5.  So if x is 1, what does y have to be?

 

Make sure you show your answer as an ordered pair:  (1, ___ ).    (You can fill in the y value.)

 

Make sense?

 

 

 

 

 

Answer 2

1st equation: 4x + y = 8   therefore,

y = 8 - 4x

 

2nd equation:  x + y = 5

substitute (8 - 4x) for y...

x + (8 - 4x) = 5  therefore,

x + 8 - 4x = 5    therefore,

8 - 3x = 5          therefore,

- 3x = -3           therefore,

3x = 3              therefore,

x = 1

 

RETURN to 2nd equation....

x + y = 5   substitute "1" for x...

1 + y = 5     therefore,

y = 4

 

Summary:   x = 1;  y = 4