find the common point of 3x+2y=4 and 2x-y=5

Question

be as detailed as possible. Thank you (:

Answer 1

You have a system of equations here.

 

3x + 2y = 4

2x -   y  = 5               The object here to solve this system is to get rid of one of the variables.

 

                                 You can do this by multiplying the 2nd equation by 2 and then add the

                                 2 equations together.

 

3x + 2y = 4           ⇒      3x + 2y = 4

2(2x - y) = 2(5)     ⇒      4x - 2y = 10       now add them together.  Notice the y's cancel

                                     7x        = 14       now divide both sides by 7

 

                                              x = 2         We need to find the y value.  Put the 2 for x into the

 

                                                                first equation and solve for y.

 

                         3x + 2y = 4

                        3(2) + 2y = 4

                          6   +  2y = 4

                         -6              -6

 

                                    2y = -2

 

                               (2y)/2 = -2/2

 

                                       y = -1

 

If x = 2 and y = -1 the common point would be the ordered pair (2,-1)

 

CHECK   put x and y values into both equations to make sure the ordered pair works in both

 

3x + 2y = 4                   2x - y = 5

 

3(2) + 2(-1) = 4             2(2) - (-1) = 5

 

   6   +  -2    = 4                4 + 1     = 5

 

                 4 = 4√                        5 = 5√

 

It works in both.

 

                                

Answer 2

Serena, you have posted several of the same

type of problem.  If you look at the others you

can use them as an example.

 

The thing to remember is that if two equations

are true then their sum or difference is also true.

That means you can add or subtract them and

come up with a new equation that is also true.

 

For example:    3 - 5 = -2     equation 1

                    -11+ 7 = -4     equation 2

                   ----------------

                     -8 + 2 = -6    equation 1 + equation 2

 

Also, for any true equation, if you multiply or divide the

entire equation by the same number you will also have

a new equation that is also true.

 

For example:   8 - 1 = 7

                    3(8-1 = 7) becomes 24 - 3 = 21

 

When solving a system of equations by elimination these are

the rules you use.

 

3x + 2y = 4           If we add these equations as they are, we

2x  -  y =  5           will not eliminate any variable, so we don't

---------------         accomplish anything.  We need one of the

                             variables to have the same coefficient in

                             both equations.  Actually, I find it easier to

                            get the same coefficient with opposite sign.

 

If we multiply the 2nd equation through by 2, we will have 2y in

the 1st equation and -2y in the 2nd equation.  We can then add

the two equations to come up with a new equation with only a

single variable, having eliminated the y variable.

 

3x + 2y = 4       equation 1

2(2x - y = 5)      2(equation 2)

 

3x + 2y = 4       equation 1

4x - 2y  = 10     2(equation 2)

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

7x + 0y = 14

7x = 14

x = 2

 

From this process we have found the value of x.

Substitute 2 in place of x in either of the original

equations and solve for y.

 

3(2) + 2y = 4

6 + 2y = 4

2y = 4-6

2y = -2

y = -1

 

Your answer, using the method "solve by elimination" is

x = 2, y = -1

 

I hope this clarifies things for you.  Good luck.  Let me

know if you have any questions.