2x + 3y = 2     x - 3y = 7  find x and y

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

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2x + 3y = 2 ........(1)

x - 3y = 7 ..........(2)

Using the elimination method, add both (1) and (2):

==> 3x = 9

==> divide by 3:

==> x = 3

Now to find y value using the substitution method, we will substitute with either (1) or (2)

x - 3y = 7

==> 3y = x-7

==> y = (x-7)/3 = (3-7)/3 = -4/3

==> y = -4/3

 

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nisarg | Student, Grade 11 | (Level 1) Valedictorian

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2x + 3y = 2  

x - 3y = 7

3x=9

x=3

x-3y=7

3-3y=7

-3y=4

y=-4/3

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jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

2x + 3y = 2    

x - 3y = 7  

First multiply everything in the bottom equation by 2

By multiplying,  you should get

2x + 3y = 2

2x - 6y = 14 now subtract 2x with 2x ( which means subtract 3y with -6y and 2 with 14 ) 

By subtracting,  you should get

9y = -12 divide both sides by 9

By dividing, you should get

Y = -12/9 simplify

Y = -4/3 which is your answer for " y "

Now plug -4/3 into one of the equation

X - 3 ( -4/3 ) = 7 multiply -3 with -4/3 

By multiplying,  you should get

X + 12/3 = 7 subtract 12/3 on both sides

By subtracting, you should get

X = 4 which is your answer for " x " 

So x = 4 and y = -4/3

kristine-612quizst's profile pic

kristine-612quizst | Student, Grade 10 | (Level 1) eNoter

Posted on

Elimination process:

         2x + 3y = 2

+       x   -  3y = 7       Eliminate 3y since 3y + -3y = 0

3x = 9

3x/3 = 9/3   divide 3x and 9 by 3 to eliminate 3

x= 3

then, substitute the value of the x to any of the given equations.

2(3) + 3y = 2

6 + 3y = 2   multiply 2 and 3

3y = 2 - 6          move 6 to the other side

3y/3 = -4/3   divide 3y and -4 by 3

y= -4/3

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Because the equations of the system are linear, we'll use the matrix formed by the coefficients of the variables to calculate the determinant of the system:

             2         3

det A =

             1         -3

 

det A = 2*(-3) - 3

det A = -6 - 3

det A = -9 different from zero.

Now, we'll calculate x:

x = det x/ det A

             2         3

det x =

             7         -3

 

det x = -6 - 21 = -27

x = -27/-9

x = 3

Now, we'll calculate y:

 

             2         2

det y =

             1         7

det y = 14 - 2

det y = 12

 

y = det y/ det A

y = 12/-9

y = -4/3

The solution of the system is: {(3 , -4/3)}

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

2x+3y = 2

x-3y =7.

Tofind x and y.

Solution:

We use substitution method.

From the 2nd equation, we get  x = 7+3y. Substuting this in the first, we get 2(7+3y) + 3y = 2.

14+6y +3y =2

14+ 9y = 2

9y = 2-14 = -12.

y = -12/9 = -4/3

Substituting y =-4/9 in 2nd equation, x-3(-4/3) = 7, x = 7+3*(-4/3) = 3

x = 3 and y = -4/3

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