Question

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) $$\begin{array}{c} 2 x-3 y=-1 \\ -4 x+6 y=2 \end{array}$$

   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)
$$\begin{array}{c}
2 x-3 y=-1 \\
-4 x+6 y=2
\end{array}$$

Algebra and Trigonometry

Judith A. Beecher,… 4th Edition

Chapter 9, Problem 5

Instant Answer

Step 1

Step 1: Rewrite the system of equations in standard form: $$\begin{array}{c} 2x - 3y = -1 \\ -4x + 6y = 2 \end{array}$$ Show more…

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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) $$\begin{array}{c} 2 x-3 y=-1 \\ -4 x+6 y=2 \end{array}$$

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Key Concepts

System of Linear Equations

A system of linear equations is a set of two or more linear equations involving the same set of variables. The goal is to find values for the variables that satisfy all the equations simultaneously, which can lead to a unique solution, no solution, or infinitely many solutions.

Dependent System

A dependent system occurs when one equation in the system is a multiple of another, meaning the equations represent the same line graphically. This results in infinitely many solutions because every point on the line is a solution to both equations.

Graphical Representation

In the context of linear equations, the graph of a dependent system is a single line. Since the two equations are identical in essence, they overlap completely when graphed, which distinguishes them from systems with distinct lines that intersect at a single point or are parallel with no intersection.

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