Match the system of equations with one of the graphs ( a ) -...

Match the system of equations with one of the graphs ( $a$ ) - $(f),$ which follow.
A.(GRAPH CANNOT COPY)
B.(GRAPH CANNOT COPY)
C.(GRAPH CANNOT COPY)
D.(GRAPH CANNOT COPY)
E.(GRAPH CANNOT COPY)
F.(GRAPH CANNOT COPY)
$$\begin{aligned}
&x-y=-5\\
&x=-4 y
\end{aligned}$$

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations with the same set of variables. The goal is to determine the values of these variables that satisfy all equations simultaneously, which corresponds to finding the point(s) where the graphs of the equations intersect.

Graphical Representation of Equations

Graphing linear equations involves plotting the lines they represent on the coordinate plane. This method visually demonstrates the relationship between the equations, showing how changes in variables affect the graph's position and slope.

Intersection of Lines

The solution to a system of linear equations is represented by the point(s) where the corresponding lines intersect. This intersection point provides the values of the variables that simultaneously satisfy all the equations in the system.

Conversion to Slope-Intercept Form

Rewriting equations in slope-intercept form (y = mx + b) helps in understanding the slope and y-intercept of each line. This form is useful for quickly graphing the equations and for analyzing the relationship between the lines, such as whether they are parallel, perpendicular, or intersect at a unique point.

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