Draw the graph
2y=4x-6; 2x=y+3
Answers
Answer:
The equations of the lines are
2y = 4x - 6
and 2x = y + 3
Or 4x - 2y = 6 ...(i)
2x - y = 3 ...(ii)
Putting x = 0 in equation (i), we get:
4 \(\times\) 0 - 2y = 6
\(\Rightarrow\) y = -3
\(\Rightarrow\) x = 0, y = -3
Putting y = 0 in equation (i), we get
4x - 2\(\times\)0 = 6
\(\Rightarrow\) x =3/2
x = 3/2, y = 0
Use the following table to draw the graph.
x 0 3/2
y -3 0
The graph of (i) can be obtained by plotting the two points A(0, -3), B(3/2, 0).
Now for the graph of the equation (ii), viz.
2x - y = 3 ....(ii)
Putting x = 0 in equation (ii), we get.
2 \(\times\) 0 - y = 3
\(\Rightarrow\) y = -3
i.e, x = 0, y = -3
Putting y = 0 in equation (ii), we get.
2x - 0 = 3
\(\Rightarrow\) x = 3/2
i.e, x = 3/2, y = 0
Use the following table to draw the graph.
x 0 3/2
y -3 0
The required graph for (i) and (ii) are as follows:
The two lines are coincident.
Hence the equations have infinitely many solutions.
Thus, the system is consistent.
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