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Draw the graphs of the following …

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Draw the graphs of the following equations 2x+3y=12 and x-y=1. Find the coordinates of the vertices of the triangle formed by the two straight line and x axis . Also calculate the area of this triangle.

Posted by Abhishek Rawat 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

{tex}2x + 3y = 12{/tex}
{tex}x = \frac{{12 - 3y}}{2}{/tex}
When y = 0, then x = 6
When y = 2, then x = 3

x	6	3
y	0	2

We have,
{tex}x - y = 1{/tex}
{tex}x = 1 + y{/tex}
When y = 0, then x = 1
When y = -1, then x = 0

x	1	0
y	0	-1

Graph of the given system is:

Clearly, the two lines intersect at {tex}A(3, 2){/tex}
We also observe that the lines meet y-axis B(0, -1) and C(0, 4)
Hence the vertices of the required triangle are {tex}A(3,2), B(0, -1)\ and\ C(0,4).{/tex}

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