Draw the graphs of the equation 5x – y = 5 and 3x – y = 3. Determine the coordinates of the vertices of the triangle formed by these lines and the y-axis.

Solution : 

The given linear equations are

5x – y = 5           ………(1)

3x – y = 3            ………(2)

From equation (1),   y = 5x – 5

When x = 1, y = 5 – 5 = 0

When x = 2, y = 10 – 5 = 5

x12
y05

From equation (2), y = 3x – 3

When x = 0, y = -3

When x = 2, y = 3

x02
y-33

Now, plot the above points on the graph, we get two lines.

We see that the line meets y-axis, the value of x is 0. In the equation 5x – y = 5, for x = 0, we get y = – 5.

Thus, the line 5x – y = 3 meets the y-axis at (0, -5).

and the line 3x – y = 3 meets the y-axis at (0, -3).

Thus, the coordinates of \(\triangle\) ACE formed by these two lines and the y-axis A(1, 0), C(0, – 3) and E(0, -5).

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