2x-3y = 8 x+2y=3 solve x and y

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To solve

2x-3y = 8......(1)

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

Solution:

We solve by substitution method using y value from eq(2) and put it in (1).

From (2) we get: y =(3-x)/2. Put this value of y in (1) and get:

2x - 3(3-x)/2 = 8. Multiply by 2.

4x-3(3-x) = 6.

4x-9+3x = 16

7x = 16+9 = 25

7x+7 =25/7

x=25/1 = 3 and 4/7.

Substituting this in (1), 2x-3y = 8, 2(25/7)-3y = 8, -3y = 8-50/7 = 6/7, y = (6/7)/(-3) = -2/7.

So (x,y) = (25/7,-2/7)

2x - 3y = 8 ... (1)

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

Multiplying equation (2) by 2 :

2x + 4y = 6 ... (3)

Subtracting equation (1) from (3):

2x - 2x + 4y + 3y = 6 - 8

7y = -2

y = -2/7

Substituting value of y in equation (2):

x + 2(-2/7) = 3

x - 4/7 = 3

x = 3 + 4/7 = 25/7

Answer:

x = -2/7, y = 25/7

We'll eliminate the unknown y, by multiplying the first equation by 2 and the second equation, by 3.

The system of equations will become:

2(2x-3y) = 16

3(x+2y) = 9

Now, we'll open the brackets and we'll add the equations from the system:

4x - 6y + 3x + 6y = 16+9

7x = 25

We'll divide by 7:

x = 25/7

We'll find y, substituting x by it's value, in any of 2 equations.

We'll substitute x in the first equation:

2x-3y = 8

50/7 - 3y = 8

-3y = 8 - 50/7

-3y = (56-50)/7

-3y = 6/7

We'll divide by -3:

y = 6/-3*7

y = -2/7

**The solution of the system is: (-2/7 , 25/7).**

2x - 3y = 8

x + 2y = 3

multiply the digits on the second equation by 2

By multiplying, your equation should look like

**2x - 3y = 8 **

**2x + 4y = 6**

Now, subtract the 2x with 2x ( so subtract -3y with 2y and 8 with 6 )

By doing that your equation should look like

**-7y = 2** now divide both sides by -7

By dividing, your equation should look like

**y = -2/7 **which is your answer for " y "

Now, plug - 2/7 into one of the equation

**2x + 4 ( -2/7 ) = 6 **multiply 4 with -2/7

By multiplying, your equation should look like

**2x - 8/7 = 6 **add 8/7 on both sides

By adding, your equation should be

**2x = 50/7 **divide both sides by 2

By dividing, your equation should look like

**x = 50/14 **simplify

**x = 25/7 **which is your answer for " x "

So, your answer is **x = 25/7 ; ****y = -2/7**

2x-3y =8......(1)

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

We will use the elimination method to solve:

First, multiply (2) by -2 and add to (1):

-7y = 2

==> **y= -2/7**

Now substitute y= -2/7 in (2):

x+ 2y= 3

x+ 2(-2/7) = 3

x -4/7= 3

Move -4/7 to the right side:

x= 3+ 4/7

x= 21/7 + 4/7 = 25/7

**x= 25/7**

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