x-2y=5 x-3y=7

Question

show work please?

Answer 1

x-2y=5               x-3y=7

 +2y=+2y

x-0=5+2y

x=5+2y

This problem says x is 5+2y, so substitute 5+2y for x in the other problem:

 

x-3y=7                   1. Put 5+2y in place of the x:

(5+2y)-3y=7           2. Now, remove the parenthesis:

5+2y-3y=7             3. Combine the y's:

 5-y= 7  (2y-3y=-y) 4. Solve for y:

-5  =-5

0-y= 2

 

- (1)y=  2

      -1

 

y=-2                       5. Now that you know y is -2, you can put it in your problems to solve for x:

 

x-3y=7                   x-2y=5

x-3(-2)=7               x-2(-2)=5

x+6= 7                  x+4= 5

   -6=-6                    -4=-4

   x=1                       x=1

Answer 2

Hello, America

 

This is a system of linear equations.  Since you did not tell me which method to use, I am going to use the ELIMINATION METHOD.  That is, I will try to get rid of one of the variables.  In this case getting rid of the X will be the best way to do this problem because it requires one calculation.  Here we go,

 

x-2y= 5

x-3y=7                I am going to multiply this by -1.  So this becomes -x+3y=-7

 

x   -2y=5

-x+3y=-7           Adding the top and the bottom

      y=-2            x and -x cancel each other out.

 

Now, I am going to substitute -2 for y into x-2y=5.

 

x-2(-2)=5

x+4     =5

   -4      -4

      x= 1

So, the answer for this system is (1, -2).  Make sure to double check your answer by plugging your answers into either of the original equations. Let me use x-3y=7

 

x-3y=7

(1)-3(-2)= 7

1+6=7

6= 6                 So, it works

 

Ok, I hope this helps.  And please, don't forget to rate my answer :)

 

D. Y. Taylor