# Draw the graphs of the following linear equations on the same graph paper: 2x + 3y = 12, x – y = 1.

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Draw the graphs of the following linear equations on the same graph paper: 2x + 3y = 12, x – y = 1.

Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis. Also, find the area of the triangle.

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Graph of the equation 2x +3y -12 = 0

we have

Thus, we have the following table for the p table for the points on the line 2x +3y = 12

Plotting points A (0, 4) , B (3, 2) on the graph paper and drawing a line passing through them we obtain graph of the equation.

Graph of the equation x - y -1

we have x - y = 1

x = 1 + y

Thus, we have the following table for the points the line x - y = 1

Plotting points  C (1, 0) and D (0, -1) on the same graph paper drawing a line passing through the m, we obtain the graph of the line represents by the equation x - y = 1

Clearly two lines intersect at A(3, 2).

The graph of time 2x +3y = 12 intersect with y axis at B (0, 4) and the graph of the line x - y =1 intersect with y axis  at C (0, -1).

So, the vertices of the triangle formed by thee two straight lines and y axis are A(3, 2) and B(0, 4) and C(0, -1)

Now,