+0  
 
0
49
3
avatar

**Solve using the linear combination method**

1.

4x + y = 4

2x + y =  6

 

 

2.

x - y = 10

5x + 2y = 12

 

 

3.

5/2x + 2y = -2

-x + y = 2

Guest Jan 19, 2018
Sort: 

3+0 Answers

 #1
avatar+82546 
+1

The linear combination method is also known as the "addition" method

 

1.    We can pick either variable to eliminate....I'll pick  y

 

4x + y = 4      (1)

2x + y =  6     multiply this through by  -1   ⇒  -2x  -  y  =  -6     (2)

 

Add (1)  and (2)

 

2x   =  - 2         divide both sides by  2

x  =  -1

 

And using  (1)  to solve for  y  we have

 

4(-1)  + y  = 4

-4 +  y   =  4       add 4 to both sides

y  =  8

 

cool cool cool

CPhill  Jan 19, 2018
 #2
avatar
0

Thank you, could I please get help on two and three?

Guest Jan 19, 2018
 #3
avatar+82546 
+1

2.

x - y = 10       multiply through by 2  ⇒  2x  - 2y  =  20   (1) 

5x + 2y = 12    (2)

 

Add  (1)  and (2)

 

7x  =  32      divide both sides by  7

x  =  32 / 7

 

Using  (1)  to solve for  y

 

(32/7)  -  y  =  10         multiply through by 7

32 - 7y  =   70             subtract 32  from both sides

-7y  =  38                   divide both sides by  -7

y  = -38/7

 

 

 

3.

5/2x + 2y = -2   multiply through by 2 to clear the fraction ⇒  5x + 4y  = -4  (1)

-x + y = 2   multiply through by  5  ⇒  -5x + 5y  = 10  (2)

 

Add  (1) and (2)

 

9y  =  6      divide through by  9

y  =  6/9  =  2/3

 

Put this into     -x  + y  =  2

-x +  (2/3)  = 2      subtract  2/3 from both sides

-x  =  2 - 2/3   =  4/3        

-x  =  4/3

x  =  -4/3

 

 

 

cool cool cool

CPhill  Jan 19, 2018

19 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details