Solve each system by graphing. Identify systems with no...

Solve each system by graphing. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.
$$
\left\{\begin{array}{l}{2 x-y=-4} \\ {4 x-2 y=6}\end{array}\right.
$$

Key Concepts

Set Notation for Solutions

Set notation is a mathematical way of expressing the solution set of a system of equations. For a system with no solution, the solution set is represented by the empty set symbol (?), while a unique solution or infinitely many solutions would be expressed with a set containing all the appropriate solution points.

Parallel Lines

Parallel lines are lines in a plane that never intersect because they have the same slope but different y-intercepts. In the context of systems of equations, if the corresponding lines are parallel, the system has no solution.

Graphing Linear Equations

Graphing linear equations involves plotting each equation on a coordinate plane and identifying the point(s) where they intersect. The graphical approach is particularly useful in understanding the nature of solutions in terms of one intersection point (unique solution), overlapping lines (infinitely many solutions), or parallel lines that never meet (no solution).

Inconsistent Systems

An inconsistent system is one in which the equations represent lines that do not intersect at any point. This means there is no set of variable values that simultaneously satisfies all equations, often indicated by parallel lines in the graphical approach.

System of Linear Equations

A system of linear equations consists of two or more equations with the same set of variables. The goal is to find values for the variables that make all equations true simultaneously. These systems can have a single solution, infinitely many solutions, or no solution at all.

Please give Ace some feedback