In Problems 15- 12 , solve each system of equations using...

In Problems 15- 12 , solve each system of equations using Cramer's Rule if it is applicable. If Cranter's Rule is nor applicable, say sa
$\left\{\begin{array}{l}x+2 y-5 \\ x-y=3\end{array}\right.$

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Key Concepts

Systems of Linear Equations

A system of linear equations consists of multiple linear equations involving the same set of variables. The objective is to find values for the variables that satisfy all the equations simultaneously, representing the point of intersection of the lines or planes described by the equations.

Cramer's Rule

Cramer's Rule is a mathematical theorem used to solve systems of linear equations with as many equations as unknowns by expressing the solution in terms of determinants of matrices. It provides a formula for each variable as the ratio of two determinants, making it a useful tool provided that the coefficient matrix has a non-zero determinant.

Determinants

A determinant is a scalar value that is computed from the elements of a square matrix. Determinants are used to assess whether a matrix is invertible; specifically in Cramer's Rule, the determinant of the coefficient matrix must be non-zero to guarantee that there is a unique solution to the system.

Applicability of Cramer's Rule

The applicability of Cramer's Rule hinges on the condition that the determinant of the coefficient matrix is not zero. If the determinant equals zero, the system either has no solution or an infinite number of solutions, rendering Cramer's Rule invalid for solving that system.

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