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

*print*Print*list*Cite

### 6 Answers

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**

2x + 3y = 2

x - 3y = 7

3x=9

x=3

x-3y=7

3-3y=7

-3y=4

y=-4/3

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

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

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)}**

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