Cramers Rule Calculator

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Example

Created on 2024-06-20Asked by Benjamin Adams (Solvelet student)

Use Cramer's Rule to solve the system of equations:

\begin{cases} 2x + 3y = 7 \\ 4x - 5y = 9 \end{cases}

Solution

Step 1: Write the given system of equations in matrix form:

\begin{bmatrix} 2 & 3 \ 4 & -5 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 7 \ 9 \end{bmatrix}.

Step 2: Compute the determinant of the coefficient matrix

A

\text{det}(A) = \begin{vmatrix} 2 & 3 \ 4 & -5 \end{vmatrix} = (2 \times -5) - (3 \times 4) = -10 - 12 = -22.

Step 3: Compute the determinants of

A_x

and

A_y

by replacing the respective columns of

A

with the constants from the right-hand side:

A_x = \begin{vmatrix} 7 & 3 \ 9 & -5 \end{vmatrix} = (7 \times -5) - (3 \times 9) = -35 - 27 = -62,

\[ A_y = \begin{vmatrix} 2 & 7Solved on Solvelet with Basic AI Model

Some of the related questions asked by Avery Harris on Solvelet

1. Solve the equations by using cramer's rule :

2x + 3y = 5

4x - y = 7

2. Apply Cramer's rule to find the solution to the system of equations:

x + y + z = 6

2x - y + z = 3

x + 2y - z = 1

DefinitionCramer's law: Cramer's law is a solution to the decision of a system of equations. It gives the formula for solving the equation of the ratio of determinants whose elements are the coefficients of the equation. Cramer's law can be used when the system of equations has only one solution and the order of the coefficient matrix is non-zero. I, in the context of mathematics, engineering, physics) - Mathematics for solving systems of equations. Note: In mathematics, Cramer's law is an exact formula used to solve a system of linear equations with multiple unknowns and is valid as long as the system has specific problem solutions.

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