The system of equations { 2 x+3 y=7 5 x-y=9 . is a system of two equations in the two va

step 1 So here we're given a couple of flammer blanks. The system of equations is a system of two equat

The system of equations { 2 x+3 y=7 5 x-y=9 . is a...

The system of equations $\left\{\begin{array}{l}{2 x+3 y=7} \\ {5 x-y=9}\end{array}\right.$ is a system of two equations in the two variables _____ and _____ To determine whether $(5,-1)$ is a solution of this system, we check whether $x=5$ and $y=-1$ satisfy each _____ in the system. Which of the following are solutions of this system? $(5,-1), \quad(-1,3), \quad(2,1)$

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Key Concepts

System of Linear Equations

A system of linear equations consists of multiple linear equations that share common variables. The goal is to find values for these variables such that every equation in the system is simultaneously satisfied. These systems are foundational in algebra and appear in various applications such as physics, engineering, and economics.

Variables

In any algebraic equation, variables represent the unknown quantities that need to be determined. In the context of systems of equations, the same variables appear across different equations, and finding their values is essential to solving the system.

Solution of a System

A solution of a system is a set of values for the variables that makes all the equations in the system true when substituted into them. For a system of linear equations, a solution corresponds to the point of intersection of the lines on a coordinate plane.

Verification by Substitution

Verification by substitution is a method used to check if a given set of values for the variables is a solution to the equations. This involves plugging the values into each equation and ensuring that the resulting numerical statements are true. It is an essential technique for confirming candidate solutions in a system.

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