System solving2x-4y = 12    x+3y = 3

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

You can use substitution to solve the system of equations

2x - 4y = 12 ...(1)

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

From (2), x + 3y = 3

=> x = 3 - 3y

Substitute this in (1)

2*(3 - 3y) - 4y = 12

=> 6 - 6y - 4y = 12

=> 6 - 10y = 12

=> 10y = -6

=> y = -6/10

x = 3 - 3y = 3 + 3*(6/10) = 3 + 18/10

=> x = 48/10

The solution of the system of equations is x = 48/10 and y = -6/10

pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

First, find a value for x using the second equation:

x = 3 - 3y

Then substitute that in to the first equation

2 (3-3y) - 4y = 12

6 - 6y - 4y = 12

- 10y = 6

y = -.6

Then you plug this back into the first equation

x + 3*-.6 = 3

x - 1.8 = 3

x = 4.8

So, x = 4.8 and y = -.6

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll solve the system using elimination method.

We'll multiply the 1st equation by 3:

6x - 12y = 36 (3)

We'll multiply the 2nd equation by 4:

4x + 12y = 12 (4)

We'll add (3) + (4):

6x - 12y + 4x + 12y  = 36 + 12

We'll combine and eliminate like terms:

10x = 48

x = 4.8

We'll substitute x in the 2nd equation:

4.8 + 3y = 3

3y = 3 - 4.8

3y = -1.8

y = -1.8/3

y = -0.6

The solution of the system is the pair (4.8 ; -0.6).

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