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Pair of Linear Equations in Two Variables
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27/05/2021 10:59 am
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Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
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27/05/2021 11:03 am
Given, the equations for graphs are x – y + 1 = 0 and 3x + 2y – 12 = 0.
For, x – y + 1 = 0 or x = 1+y
x \(\rightarrow\) 0, 1, 2
y \(\rightarrow\) 1, 2, 3
For, 3x + 2y – 12 = 0 or x = (12-2y)/3
x \(\rightarrow\) 4, 2, 0
y \(\rightarrow\) 0, 3, 6
Hence, the graphical representation of these equations is as follows
From the figure, it can be seen that these lines are intersecting each other at point (2, 3) and x-axis at (-1, 0) and (4, 0). Therefore, the vertices of the triangle are (2, 3), (-1, 0), and (4, 0).