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# Help! System of equations 3 questions

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**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

Jan 19, 2018

#1
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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   Jan 19, 2018
#2
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Thank you, could I please get help on two and three?

Guest Jan 19, 2018
#3
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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   Jan 19, 2018