Solve the following only by SUBSTITUTION method: x=y-6 and 3x+2y=2

justaguide | College Teacher | (Level 2) Distinguished Educator

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The following system of equations has to be solved:

x = y - 6 ...(1)

3x + 2y = 2 ...(2)

From (1) x = y - 6

Substitute for x in (2)

=> 3x + 2y = 2

=> 3(y - 6) + 2y = 2

=> 3y - 18 + 2y = 2

=> 5y = 20

=> y = 4

Substitute y = 4 in (1)

=> x = 4 - 6 = -2

The solution of the set of equations is x = -2 and y = 4

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The system of equations x=y-6 and 3x+2y=2 has to be solved for x. Start with the equation 3x+2y=2 and express x in terms of y.

3x+2y=2

3x = 2 - 2y

x = (2 - 2y)/3

Substitute this in the equation x = y - 6

(2 - 2y)/3 = y - 6

2 - 2y = 3y - 18

5y = 20

y = 20/5 = 4

x = (2 - 8)/3 = -6/3 = -2

The solution of the system of equations is x = -2 and y = 4

anthonytuition1 | Student | eNotes Newbie

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x=y-6

=>3x=3y-18

=>3y-18+2y=2

=>5y-18=2

=>5y=2+18

=>5y=20

=>y=20/5

=>y=4

x=y-6

=>x=4-6

=>x=-2

bhalachandra | College Teacher | (Level 1) eNoter

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The  given  equations  are:

x = y - 6                            ...  (1)

3x + 2y = 2                       ...  (2)

Substituting  (1)  in  (2),  we  get

3(y-6) + 2y = 2

=>    3y - 18 + 2y = 2

=>    5y - 18 = 2

=>    5y = 2 + 18

=>    5y = 20

=>    y = 4                                     ... (3)

Substituting  y = 4  in(1),  we  get

x = 4 - 6,   that  is  x = -2             ... (4)

From (3)  and  (4),  X = -2   AND  Y = 4.