Math, asked by thapaadarsh221, 2 days ago

prove graphically that systems of equations 6x+4y=2,3x+2y=1 is consistent and dependent​

Answers

Answered by mathdude500
3

\large\underline{\sf{Solution-}}

Given pair of linear equations are

\red{\rm :\longmapsto\:6x + 4y = 2}

and

\red{\rm :\longmapsto\:3x + 2y = 1}

Consider Equation (1)

\red{\rm :\longmapsto\:6x + 4y = 2}

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

 \red{\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 0.5 \\ \\ \sf  - 2 & \sf 3.5 \\ \\ \sf  - 4 & \sf 6.5 \end{array}} \\ \end{gathered}}

➢ Now draw a graph using the points

➢ See the attachment graph.

Consider Equation (2)

\green{\rm :\longmapsto\:3x + 2y = 1}

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

 \green{\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 0.5 \\ \\ \sf  - 2 & \sf 3.5 \\ \\ \sf  - 4 & \sf 6.5 \end{array}} \\ \end{gathered}}

➢ Now draw a graph using the points

➢ See the attachment graph.

Hence, From graph we verified that given pair of lines are dependent and system of equations is consistent.

Attachments:
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