Question

find the solution to the given pair of linear equations by graphical method 2x+y=5,x+y=4
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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

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

Given pair of linear equations are

• 2x + y = 5

• x + y = 4

Consider

• The linear equation 2x + y = 5

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

$\rm :\longmapsto\:2 \times 0 + y = 5$

$\rm :\longmapsto\: 0 + y = 5$

$\bf\implies \:y = 5$

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

$\rm :\longmapsto\:2x + 0 = 5$

$\rm :\longmapsto\:2x = 5$

$\bf\implies \:x = 2.5$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 5 \\ \\ \sf 2.5 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 5) & (2.5 , 0)

➢ See the attachment graph. (Blue line)

Consider,

• The line x + y = 4

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

$\rm :\longmapsto\:0 + y = 4$

$\bf\implies \:y = 4$

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

$\rm :\longmapsto\:x + 0 = 4$

$\bf\implies \:x = 4$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 4 \\ \\ \sf 4 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 4) & (4 , 0)

➢ See the attachment graph. (Red line)

Hence

• From graph, we conclude that x = 1 and y = 3