Draw the graphs of the equations $5 x - y = 5$ and $3 x - y = 3$ . Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.

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Solution

For the equation $3 x - y = 3$
$y = 3 x - 3$

If $x = 0, y = - 3$
For $x = 1, y = 0$
For $x = 2, y = 3$
$x$ $0$ $1$ $2$
$y$ $- 3$ $0$ $3$
For the equation $5 x - y = 5$
$\Rightarrow y = 5 x - 5$

If $x = 0, y = - 5$
For $x = 1, y = 0$
For $x = 2, y = 5$

$x$ $0$ $1$ $2$
$y$ $- 5$ $0$ $5$

Plotting the equations on the graph, we get $Δ A C E$ with $A (1, 0), C (0, - 3),$ and $E (0, - 5)$

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Draw the graphs of the equations 5x−y=5 and 3x−y=3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.

For the equation 3x−y=3y=3x−3If x=0, y=−3For x=1, y=0For x=2, y=3 x0 1 2 y−3 0 3 For the equation 5x−y=5⇒y=5x−5If x=0, y=−5For x=1, y=0For x=2, y=5 x0 1 2 y −50 5 Plotting the equations on the graph, we get ΔACE with A(1,0), C(0,−3), and E(0,−5)

Draw the graphs of the equations $5 x - y = 5$ and $3 x - y = 3$ . Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.