Question

3x-2y=5/2 ; 1/3x+3y=-4/3 crame's rule​

Answer 1

Answer:

$\boxed{x=\frac{1}{2}} \: and \: \boxed{y = \frac{-1}{2}}$ is the solution of the given simultaneous equations.

Step-by-step-explanation:

NOTE: Kindly refer to the attachment first.

Additional Information:

1. Linear Equations in two variables:

The equation with the highest index ( degree ) 1 is called as linear equation. If the equation has two different variables, it is called as 'linear equation in two variables'.

The general form of linear equation in two variables is

ax + by + c = 0

Where, a, b, c are real numbers and

a ≠ 0, b ≠ 0.

2. Solution of a Linear Equation:

The value of the given variable in the given linear equation is called the solution of the linear equation.

3. Determinant Method ( Carmer's Rule ):

1. Determinant method is one of the methods of solving simultaneous equations.

2. This method was introduced by a mathematician Gabriel Cramer. So, it is also known as Carmer's Rule.

3. It is based on determinants.

4. The constant term of given linear equation is transferred to right hand side. Therefore, the general form of Carmer's rule for simultaneous equations is

ax + by = c

Where, a, b, c are real numbers and

a ≠ 0, b ≠ 0.

5. First, determinant D is calculated and then ${D}_{x} \: and \:{D}_{y}$ are calculated step-by-step.

6. By using Carmer's rule values of x and y ( the variables used in the given equations ) are calculated.

7. Carmer's rule is as follows:

$\boxed{x =\frac{D_x}{D}}$

$\boxed{y =\frac{D_y}{D}}$