Question
Solve graphically that the following system of equation has infinitely many solutions:
x - 2y + 11 = 0
3x - 6y + 33 = 0
✓
Answer
The given equations are
x - 2y + 11 = 0 .......(i)
3x - 6y + 33 = 0 ..........(ii)
Putting x = 0 in equation (i), we get,
⇒ 0 - 2y = -11
$\Rightarrow\text{y}=\frac{11}{2}$
$\Rightarrow\text{x}=0,\ \text{y}=\frac{11}{2}$
Putting y = 0 in equation (i), we get,
⇒ x - 2 × 0 = -11
⇒ x = -11
⇒ x = -11, y = 0
Use the following table to draw the graph,
Draw the graph by plotting the two points $\text{A}\Big(0,\frac{11}{2}\Big),$ B(-11, 0) from table.
Graph of the equation,
3x - 6y = -33 .......(ii)
Putting x = 0 in equation (ii), we get,
⇒ 3 × 0 - 6y = -33
$\Rightarrow\text{y}=\frac{11}{2}$
$\Rightarrow\text{x}=0,\text{y}=\frac{11}{2}$
Putting y = 0 in equation (ii), we get,
⇒ 3x - 6 × 0 = -33
⇒ x = -11
⇒ x = -11, y = 0
Use the following table to draw the graph.
Draw the graph by plotting the two points $\text{C}\Big(0,\frac{11}{2}\Big),$ (11, 0) from table. Thus the graph of the two equations are coincide Consequently, every solution of one equation is a solution of the other.
Hence the equations have infinitely many solutions.
x - 2y + 11 = 0 .......(i)
3x - 6y + 33 = 0 ..........(ii)
Putting x = 0 in equation (i), we get,
⇒ 0 - 2y = -11
$\Rightarrow\text{y}=\frac{11}{2}$
$\Rightarrow\text{x}=0,\ \text{y}=\frac{11}{2}$
Putting y = 0 in equation (i), we get,
⇒ x - 2 × 0 = -11
⇒ x = -11
⇒ x = -11, y = 0
Use the following table to draw the graph,
|
x
|
0
|
-11
|
|
y
|
$\frac{11}{2}$
|
0
|
Graph of the equation,
3x - 6y = -33 .......(ii)
Putting x = 0 in equation (ii), we get,
⇒ 3 × 0 - 6y = -33
$\Rightarrow\text{y}=\frac{11}{2}$
$\Rightarrow\text{x}=0,\text{y}=\frac{11}{2}$
Putting y = 0 in equation (ii), we get,
⇒ 3x - 6 × 0 = -33
⇒ x = -11
⇒ x = -11, y = 0
Use the following table to draw the graph.
|
x
|
0
|
-11
|
|
y
|
$\frac{11}{2}$
|
0
|
Hence the equations have infinitely many solutions.
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