+0  
 
0
256
1
avatar

Solve alebratically the simultaneous equation 

x^2 + y^2 = 25 

y - 2x = 5

 

please explain every step 

Guest Aug 21, 2017

Best Answer 

 #1
avatar+7324 
+5

Here's how to do it using substitution. There might be a quicker way though....

 

The problem tells us...

y - 2x  =  5               Add  2x  to both sides of this equation.

y  =  5 + 2x

 

The problem tells us...

x2 + y2  =  25                  And since  y = 5 + 2x  , we can replace  y  with  5 + 2x  .

x2 + (5 + 2x)2  =  25

x2 + (5 + 2x)(5 + 2x)  =  25                                 Multiply out the parenthesees.

x2 + (5)(5) + (5)(2x) + (2x)(5) + (2x)(2x)  =  25

x2 + 25 + 10x + 10x + 4x2  =  25                        Combine like terms.

5x2 + 25 + 20x  =  25                                         Subtract  25  from both sides of the equation.

5x2 + 20x  =  0               Factor out an  x  from both terms.

x(5x + 20)  =  0              Set each factor equal to  0  and solve for  x  .

 

x  =  0     or     5x + 20  =  0     Subtract  20  from both sides.

                       5x  =  -20          Divide both sides by  5  .

                       x  =  -4

 

Now plug these values for  x  into the second equation given. (The first one will give you two answers for  y  , but only one answer for  y  works in the second equation.)

 

y - 2x  =  5       Plug in  0  for  x  .

y - 2(0)  =  5

y - 0  =  5

y  =  5

                        

y - 2x  =  5       Plug in  -4  for  x  .

y - 2(-4)  =  5

y - -8  =  5

y + 8  =  5        Subtract  8  from both sides.

    y  =  -3

So the two solutions are:

x = 0,  y = 5          and          x = -4, y = -3

hectictar  Aug 21, 2017
 #1
avatar+7324 
+5
Best Answer

Here's how to do it using substitution. There might be a quicker way though....

 

The problem tells us...

y - 2x  =  5               Add  2x  to both sides of this equation.

y  =  5 + 2x

 

The problem tells us...

x2 + y2  =  25                  And since  y = 5 + 2x  , we can replace  y  with  5 + 2x  .

x2 + (5 + 2x)2  =  25

x2 + (5 + 2x)(5 + 2x)  =  25                                 Multiply out the parenthesees.

x2 + (5)(5) + (5)(2x) + (2x)(5) + (2x)(2x)  =  25

x2 + 25 + 10x + 10x + 4x2  =  25                        Combine like terms.

5x2 + 25 + 20x  =  25                                         Subtract  25  from both sides of the equation.

5x2 + 20x  =  0               Factor out an  x  from both terms.

x(5x + 20)  =  0              Set each factor equal to  0  and solve for  x  .

 

x  =  0     or     5x + 20  =  0     Subtract  20  from both sides.

                       5x  =  -20          Divide both sides by  5  .

                       x  =  -4

 

Now plug these values for  x  into the second equation given. (The first one will give you two answers for  y  , but only one answer for  y  works in the second equation.)

 

y - 2x  =  5       Plug in  0  for  x  .

y - 2(0)  =  5

y - 0  =  5

y  =  5

                        

y - 2x  =  5       Plug in  -4  for  x  .

y - 2(-4)  =  5

y - -8  =  5

y + 8  =  5        Subtract  8  from both sides.

    y  =  -3

So the two solutions are:

x = 0,  y = 5          and          x = -4, y = -3

hectictar  Aug 21, 2017

11 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.