Without graphing, decide. a. Are the graphs of the equations...

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}8 y+6 x=4 \\ 4 y-2=3 x\end{array}\right.$

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more equations involving the same set of variables. The goal is to determine the values of the variables that satisfy all equations simultaneously. This concept is fundamental in algebra and is used to model and solve problems where multiple conditions must be met at the same time.

Graphical Interpretation of Linear Systems

When linear equations are graphed, each equation represents a line in the coordinate plane. The solution to the system is the point or points where the lines intersect. If the lines intersect at a single point, the system has a unique solution; if they are parallel, there is no solution; and if the lines are coincident (identical), there are infinitely many solutions.

Slope-Intercept Form

The slope-intercept form, written as y = mx + b, expresses a linear equation where 'm' is the slope and 'b' is the y-intercept. Converting equations into this form makes it easier to compare their slopes and intercepts, which is essential for determining the relationship between the lines—such as whether they are parallel, identical, or intersect at a single point.

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