In Exercises 11-42, solve each system by graphing. If there...

In Exercises $11-42,$ solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets.
$$\left\{\begin{array}{l}
y=3 x-4 \\
y=-2 x+1
\end{array}\right.$$

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Key Concepts

Point of Intersection

The point of intersection is the set of coordinates where the graphs of the equations meet. It represents the common solution to the system of equations, providing the values for the variables that satisfy all equations simultaneously.

System of Linear Equations

A system of linear equations is a collection of two or more linear equations involving the same set of variables. The solution to the system is the set of variable values that satisfies every equation simultaneously, representing the point(s) where the lines intersect when graphed.

Graphing Method

The graphing method involves plotting each linear equation on the same coordinate plane as a straight line. The solution to the system is then found by identifying the point of intersection between the lines. This visual approach helps in understanding the relationship between the equations and verifying the solution.

Set Notation

Set notation is a mathematical way to describe the solution set of an equation or system of equations. It is used to clearly and concisely represent the collection of all possible values that solve the system, whether it is a unique point, no solution, or infinitely many solutions.

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