# solve the system: x-2y = 5 2x-y = 3solve the system: x-2y = 5 2x-y = 3

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You may also consider the alternative method, that uses determinants, such that:

x-2y = 5

2x-y = 3

Form the determinant of the system such that:

=

You need to find the variable x such that:

You need to find the variable y such that:

**Hence, evaluating the solutions to the system yields and .**

x-2y = 5 .........(1)

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

To solve the system , we will use the elimination method:

multiply (1) by -2 and add to (2);

==>-2x + 4y = -10

==> 2x - y = 3

==> 3y = -7

==> y= -7/3

==> x = 2y + 5

= 2(-7/3) + 5 = -14/3 + 15/3 = 1/3

==> x = 1/3

To determine the solutions of the system, we'll use the substitution method. We'll note the equatios of the system as:

x-2y = 5 (1)

2x-y = 3 (2)

We'll add 2y both sides in (1):

x = 2y + 5 (3)

We'll substitute (3) into (2):

2( 2y + 5) - y = 3

We'llremove the brackets;

4y + 10 - y = 3

We'll combine like terms:

3y = 3-10

3y = -7

We'll divide by 3:

**y = -7/3**

We'll substitute y in (3):

x = 2(-7/3) + 5

x = -14/3 + 5

x = (-14+15)/3

**x = 1/3**

**The solution of the system is: {(1/3 ; -7/3)}.**

x-2y =5.........(1) and 2x-y = 3............(2)

We can solve the equation by elimination:

(1) - 2*(2) eliminates y:

(x-2y) - 2(2x-y) = 5-2*3 = -1

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

x-4x = -1

-3x = -1. Divide by 3.

x = -1/-3 = 1/3.

(2)-2*(1) eliminates x and we can solve for y:

2x-y - 2(x-2y) = 3-2*5 = 3-10 = -7

-y+4y = -7

3y = -7. Divide by 3

3y/3 = -7/3

y = -7/3.

Threfore x = 1/3 and y = -7/3.

Given:

x - 2y = 5 ... (1)

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

Multiplying equation (1) by 2:

2x - 4y = 10 ... (3)

Subtracting equation (3) from (2):

2x - 2x - y + 4y = 3 - 10

==> 3y = - 7

Dividing both sides by 3:

y = -7/3

Substituting this value of y in equation (1)

x - 2*(-7/3) = 5

==> x + 14/3 = 5

==> x = 5 - 14/3 = 1/3

Answer:

x = 1/3

y = -7/3