Question

Draw the graphs of 2y=4x-6,2x= y+3 and determine whether this system of linear equations has unique solution or not . please answer my question tennetiraj sir​

Answer 1

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

Given pair of lines are

$\rm :\longmapsto\:2y = 4x - 6 - - - (1)$

and

$\rm :\longmapsto\:2x = y + 3 - - - (2)$

Consider, Equation (1), we have

$\rm :\longmapsto\:2y = 4x - 6$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:2y = 4 \times 0 - 6$

$\rm :\longmapsto\:2y = - 6$

$\bf\implies \:y = - 3$

Substituting 'x = 1' in the given equation, we get

$\rm :\longmapsto\:2y = 4 \times 1 - 6$

$\rm :\longmapsto\:2y = 4 - 6$

$\rm :\longmapsto\:2y = - 2$

$\bf\implies \:y = - 1$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 3 \\ \\ \sf 1 & \sf - 1 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.

Now,

Consider, equation (2), we have

$\rm :\longmapsto\:2x = y + 3$

Substituting 'y = 1' in the given equation, we get

$\rm :\longmapsto\:2x = 1 + 3$

$\rm :\longmapsto\:2x = 4$

$\bf\implies \:x = 2$

Substituting 'y = 3' in the given equation, we get

$\rm :\longmapsto\:2x = 3 + 3$

$\rm :\longmapsto\:2x = 6$

$\bf\implies \:x = 3$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 2 & \sf 1 \\ \\ \sf 3 & \sf 3 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.

From graph, we conclude that

● The given pair of lines neither have unique solution nor no solution.

● These are coincident lines, so have infinitely many solutions.

Answer 2

Answer:

Oh my sweet sister

so sweet of you dear.

Thanks for telling me

Step-by-step explanation: