Question

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

Answer 1

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

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.