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Solve the following pair of equations …

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Solve the following pair of equations graphically 2x+3y=12, x-y-1=0. Shade the region between the two lines representd by the above equation and the x-axis.
  • 1 answers

Sia ? 6 years, 4 months ago

2x + 3 y = 12
3y = 12 - 2x 
or, {tex}y = \frac { 12 - 2 x } { 3 }{/tex} 
If x = 0, we have y = 4
If x = 6,we have y = 0
If x = 3 , we have y = 2
The solution table is as follows:

<th scope="row">x</th> <th scope="row">y</th>
0 6 3
4 0 2

x - y = 1
or,  y = x - 1
If x = 0, we have y = -1
If x = 1, we have y = 0
If x = 3, we have y = 2
The solution table is as follows:

<th scope="row">x</th> <th scope="row">y</th>
0 1 3
-1 0 2

Plotting the above points and drawing the lines joining them, we get the following graph.

The two lines intersect each other at point (3, 2).
Hence, x = 3 and y = 2.
{tex}\triangle A B C{/tex} is the region between the two lines represented by the given equations and the X-axis.

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