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.
$$\left\{\begin{array}{l}
2 x-y=0 \\
y=2 x
\end{array}\right.$$

Key Concepts

Set Notation for Solutions

Set notation is a concise way of expressing the collection of all possible solutions to an equation or system of equations. This method of representation is commonly used in mathematics to denote specific or infinite sets of solutions clearly.

Infinite Solutions and Coincident Lines

When two linear equations represent the same line, they are said to be coincident. This condition results in an infinite number of solutions because every point on the line satisfies both equations, illustrating that the system does not constrain the solution to a single point.

System of Linear Equations

A system of linear equations consists of two or more equations that share the same set of variables. The goal is to find values for these variables that satisfy all the equations simultaneously. In the context of algebra, this is a fundamental concept used to understand relationships between linear quantities.

Graphing Linear Equations

Graphing linear equations involves representing each equation as a line in the coordinate plane. This technique provides a visual representation of the equations, making it easier to identify points of intersection and understand how the equations relate to one another.

Intersection of Lines

The point where two plotted lines intersect represents the solution to a system of linear equations. In cases where the lines intersect at a single point, the system has a unique solution; if the lines do not intersect, there is no solution; and if the lines coincide, there are infinitely many solutions.

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