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,
$\Rightarrow 0 - 2y = -11$
$\Rightarrow\text{y}=\frac{11}{2}$
$\Rightarrow\text{x}=0,\ \text{y}=\frac{11}{2}$
Putting $y = 0$ in equation $(i)$, we get,
$\Rightarrow x - 2 \times 0 = -11$
$\Rightarrow x = -11$
$\Rightarrow x = -11, y = 0$
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,
$\Rightarrow 3 \times 0 - 6y = -33$
$\Rightarrow\text{y}=\frac{11}{2}$
$\Rightarrow\text{x}=0,\text{y}=\frac{11}{2}$
Putting $y = 0$ in equation $(ii)$, we get,
$\Rightarrow 3x - 6 \times 0 = -33$
$\Rightarrow x = -11$
$\Rightarrow x = -11, y = 0$
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,
$\Rightarrow 0 - 2y = -11$
$\Rightarrow\text{y}=\frac{11}{2}$
$\Rightarrow\text{x}=0,\ \text{y}=\frac{11}{2}$
Putting $y = 0$ in equation $(i)$, we get,
$\Rightarrow x - 2 \times 0 = -11$
$\Rightarrow x = -11$
$\Rightarrow x = -11, y = 0$
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,
$\Rightarrow 3 \times 0 - 6y = -33$
$\Rightarrow\text{y}=\frac{11}{2}$
$\Rightarrow\text{x}=0,\text{y}=\frac{11}{2}$
Putting $y = 0$ in equation $(ii)$, we get,
$\Rightarrow 3x - 6 \times 0 = -33$
$\Rightarrow x = -11$
$\Rightarrow x = -11, y = 0$
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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