# SystemSolve the system 2x + y = 3 3y - 2x = 2

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We have to solve:

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

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

From (1), y = 3 - 2x

Substitute in (2)

3(3 - 2x) - 2x = 2

=> 9 - 6x - 2x = 2

=> 8x = 7

=> x = 7/8

y = 3 - 7/4

=> 5/4

**The required solution is x = 7/8 and y = 5/4**

To solve this, let us use the first equation to find a value for y. We get

y = 3 - 2x

Now, we substitute that value into the second equation.

3 (3 - 2x) - 2x = 2

9 - 6x - 2x = 2

Subtract 9 from both sides and get

-6x - 2x = -7

Which is the same as

-8x = -7

Divide both sides by -8 and get

x = .875

Substitute this back into the first equation to find y

2(.875) + y = 3

1.75 + y = 3

y = 1.25

**x = .875 and y = 1.25**

We'll re-write the equations:

2x + y = 3

-2x + 3y = 2

We'll use the matrix to solve the system. We'll form the matrix of the system, using the coefficients of x and y:

[2 1]

A =

[-2 3]

We'll calculate the determinant of the system:

detA = 6 + 2 = 8

Since det A is not zero, the system is determinated and it will have only one solution.

x = det X/detA

|3 1|

det X =

|2 3|

detX =9 - 2 = 7

x = det X/detA

x = 7/8

We'll calculate y:

|2 3|

det Y =

|-2 2|

det Y = 4 + 6

det Y = 10

y = detY/detA

y = 10/8

y = 5/4

The solution of the system is: (7/8 , 5/4).