Draw the graph of \[x + y = 11\]and\[x – y = 5\]. Find the solution of the pair of linear equations.

317.1k+ views

Hint: The two equations are given in the question, so firstly find the common set of points in the two equations, it can be found by adding or subtracting the equations. After finding the first pair of points, then assuming the values to find the variables x and y, then it could be possible to plot the graph.
Given
The equations \[x + y = 11\] …… (1)
\[x – y = 5\] …… (2)
Now we are adding the two equation then we will get,
\[
\Rightarrow x + y + x – y = 11 + 5\\
\Rightarrow 2x = 16\\
\Rightarrow x = 8\\
\Rightarrow y = 3
\]
Let one of the set of points to plot the line will be (8, 3). Assuming the values further, to find the points.
Let \[x = 11\], then value of y will be
\[
\Rightarrow 11 + y = 11\\
\Rightarrow y = 0
\]
Let \[x = 0\], then value of y will be
\[
\Rightarrow 0 + y = 11\\
\Rightarrow y = 11
\]
Similarly, we are taking the values for the equation 2, one of the set of points will be (8,3)
Let \[x = 5\], then value of y will be
\[
\Rightarrow 5 – y = 5\\
\Rightarrow y = 0
\]
Let \[x = 0\], then value of y will be
\[
\Rightarrow 0 – y = 5\\
\Rightarrow y = – 5
\]
If we draw the graph for the two equations according to the assuming values, then the two lines will be intersect at (8,3) Therefore, the graph is drawn for the given equation.
Note: It should be kept in mind that the two equations will consist of a common set of points, it just means that the lines of two equations will intersect at a point, so while assuming the values to find the points we need to be careful about it.

Given

The equations \[x + y = 11\] …… (1)

\[x – y = 5\] …… (2)

Now we are adding the two equation then we will get,

\[

\Rightarrow x + y + x – y = 11 + 5\\

\Rightarrow 2x = 16\\

\Rightarrow x = 8\\

\Rightarrow y = 3

\]

Let one of the set of points to plot the line will be (8, 3). Assuming the values further, to find the points.

Let \[x = 11\], then value of y will be

\[

\Rightarrow 11 + y = 11\\

\Rightarrow y = 0

\]

Let \[x = 0\], then value of y will be

\[

\Rightarrow 0 + y = 11\\

\Rightarrow y = 11

\]

Similarly, we are taking the values for the equation 2, one of the set of points will be (8,3)

Let \[x = 5\], then value of y will be

\[

\Rightarrow 5 – y = 5\\

\Rightarrow y = 0

\]

Let \[x = 0\], then value of y will be

\[

\Rightarrow 0 – y = 5\\

\Rightarrow y = – 5

\]

If we draw the graph for the two equations according to the assuming values, then the two lines will be intersect at (8,3) Therefore, the graph is drawn for the given equation.

Note: It should be kept in mind that the two equations will consist of a common set of points, it just means that the lines of two equations will intersect at a point, so while assuming the values to find the points we need to be careful about it.

Last updated date: 02nd Sep 2023

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