21-50= Solving a System of Equations Solve the system, or...

$21-50=$ Solving a System of Equations Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in the ordered-pair form given in Example $6 .$

$8 s-3 t=-3$
$5 s-2 t=-1$

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Key Concepts

System of Linear Equations

A system of linear equations involves two or more equations with common variables where the goal is to find a set of variable values that simultaneously satisfy all the equations. It forms the basis for solving problems in algebra and modeling situations where multiple conditions must be met at the same time.

Elimination Method

The elimination method is a technique for solving a system of equations by adding or subtracting the equations to cancel out one of the variables. This allows one to reduce a system of equations to a single equation in one variable, making it easier to solve and then back substitute to find the remaining variable.

Substitution Method

The substitution method involves solving one equation for one variable and then substituting that expression into another equation. This process reduces the number of variables in the second equation, thereby simplifying the solution process and leading to a single-variable equation that can be solved directly.

Ordered-Pair Representation

Ordered-pair representation is a way of expressing the solution of a two-variable system, where the solution is written in the form (s, t). This notation concisely communicates the unique or general solution set that satisfies all the equations in the system.

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