We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
248
2
avatar+1405 

Help me Please

 

Solve the Systems of equations

 

{x+y=5}

{x2+y2=13}

 Mar 6, 2018

Best Answer 

 #1
avatar+7604 
+3

x + y  =  5     Subtract  y  from both sides of this equation.

x  =  5 - y      Use this value of  x  in the second equation.

 

x2 + y2   =  13

(5 - y)2 + y2   =  13

(5 - y)(5 - y)  +  y2   =  13

25 - 10y + y2  +  y2   =  13

25 - 10y + 2y2   =  13              Subtract  13  from both sides of the equation.

12 - 10y + 2y2   =  0                Rearrange.

2y2 - 10y + 12   =  0                Divide through by  2 .

y2 - 5y + 6   =   0                     Factor left side.

(y - 3)(y - 2)  =  0                      Set each factor equal to zero.

y - 3  =  0     or     y - 2  =  0

y  =  3          or     y  =  2

 

Use both of these values of  y  to find  x .

 

When   y  =  3 ,   x  =  5 - y  =  5 - 3  =  2

 

When   y  =  2 ,   x  =  5 - y  =  5 - 2  =  3

 

So...

 

One solution is   x = 2   and   y = 3

Another solution is   x = 3   and   y = 2

 

The solution set is  { (2, 3), (3, 2) }

 Mar 6, 2018
 #1
avatar+7604 
+3
Best Answer

x + y  =  5     Subtract  y  from both sides of this equation.

x  =  5 - y      Use this value of  x  in the second equation.

 

x2 + y2   =  13

(5 - y)2 + y2   =  13

(5 - y)(5 - y)  +  y2   =  13

25 - 10y + y2  +  y2   =  13

25 - 10y + 2y2   =  13              Subtract  13  from both sides of the equation.

12 - 10y + 2y2   =  0                Rearrange.

2y2 - 10y + 12   =  0                Divide through by  2 .

y2 - 5y + 6   =   0                     Factor left side.

(y - 3)(y - 2)  =  0                      Set each factor equal to zero.

y - 3  =  0     or     y - 2  =  0

y  =  3          or     y  =  2

 

Use both of these values of  y  to find  x .

 

When   y  =  3 ,   x  =  5 - y  =  5 - 3  =  2

 

When   y  =  2 ,   x  =  5 - y  =  5 - 2  =  3

 

So...

 

One solution is   x = 2   and   y = 3

Another solution is   x = 3   and   y = 2

 

The solution set is  { (2, 3), (3, 2) }

hectictar Mar 6, 2018
 #2
avatar+1405 
+2

Thanks Hect

 Mar 6, 2018

20 Online Users

avatar
avatar
avatar