Math, asked by vvgs0081, 5 hours ago

show graphically that the system of equations 2x+3y=10; 2x +5y=12 is consistent​

Answers

Answered by mathdude500
1

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

Given equation of lines are

\rm :\longmapsto\:2x + 3y = 10 -  -  -  - (1)

and

\rm :\longmapsto\:2x + 5y = 12 -  -  -  - (2)

Consider Equation (1)

\rm :\longmapsto\:2x + 3y = 10

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

\rm :\longmapsto\:2x + 3(0) = 10

\rm :\longmapsto\:2x  = 10

\rm :\longmapsto\:x  = 5

Substituting 'y = 2' in the given equation, we get

\rm :\longmapsto\:2x + 3(2) = 10

\rm :\longmapsto\:2x + 6 = 10

\rm :\longmapsto\:2x  = 10  - 6

\rm :\longmapsto\:2x  = 4

\rm :\longmapsto\:x  = 2

Substituting 'y = 4' in the given equation, we get

\rm :\longmapsto\:2x + 3(4) = 10

\rm :\longmapsto\:2x + 12 = 10

\rm :\longmapsto\:2x = 10  - 12

\rm :\longmapsto\:2x =  - 2

\rm :\longmapsto\:x =  - 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 5 & \sf 0 \\ \\ \sf 2 & \sf 2 \\ \\ \sf  - 1 & \sf 4 \end{array}} \\ \end{gathered}

➢ Now draw a graph using the above points

➢ See the attachment graph.

Now,

Consider equation (2)

\rm :\longmapsto\:2x + 5y = 12

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

\rm :\longmapsto\:2x + 5(0) = 12

\rm :\longmapsto\:2x = 12

\rm :\longmapsto\:x = 6

Substituting 'y = 2' in the given equation, we get

\rm :\longmapsto\:2x + 5(2) = 12

\rm :\longmapsto\:2x + 10= 12

\rm :\longmapsto\:2x= 12 - 10

\rm :\longmapsto\:2x= 2

\rm :\longmapsto\:x= 1

Substituting 'y = 4' in the given equation, we get

\rm :\longmapsto\:2x + 5(4) = 12

\rm :\longmapsto\:2x + 20= 12

\rm :\longmapsto\:2x= 12 - 20

\rm :\longmapsto\:2x=  - 8

\rm :\longmapsto\:x=  - 4

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 6 & \sf 0 \\ \\ \sf 1 & \sf 2 \\ \\ \sf  - 4 & \sf 4 \end{array}} \\ \end{gathered}

➢ Now draw a graph using these points.

➢ See the attachment graph.

From graph,

We conclude that the given lines are intersecting,

So, system of equation is consistent.

Attachments:
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