Question
Solve the following systems of equations graphically:
$x + y = 6$
$x - y = 2$
✓
Answer
The given equations are
$x + y = 6 .......(i)$
$x - y = 2 ..........(ii)$
Putting $x = 0$ in equation $(i)$, we get,
$\Rightarrow 0 + y = 6$
$\Rightarrow y = 6$
$x = 0, y = 6$
Putting $y = 0$ in equation $(i)$, we get,
$\Rightarrow x + 0 = 6$
$\Rightarrow x = 6$
$x = 6, y= 0$
Use the following table to draw the graph.
Draw the graph by plotting the two points $A(0, 6)$ and $B(6, 0)$ from table.
Graph of the equation,
$x - y = 2 .......(ii)$
Putting $x = 0$ in equation $(ii)$ we get,
$\Rightarrow 0 - y = 2$
$\Rightarrow y = -2$
$\Rightarrow x = 0, y = -2$
Putting $y = 0$ in equation $(ii)$, we get,
$\Rightarrow x - 0 = 2$
$\Rightarrow x = 2$
$\Rightarrow x = 2, y = 0$
Use the following table to draw the graph.
Draw the graph by plotting the two points $C(0, -2)$ and $D(2, 0)$ from table.
The two lines intersect at points$ P(4, 2).$
Hence $x = 4, y = 2$ is the solution.
$x + y = 6 .......(i)$
$x - y = 2 ..........(ii)$
Putting $x = 0$ in equation $(i)$, we get,
$\Rightarrow 0 + y = 6$
$\Rightarrow y = 6$
$x = 0, y = 6$
Putting $y = 0$ in equation $(i)$, we get,
$\Rightarrow x + 0 = 6$
$\Rightarrow x = 6$
$x = 6, y= 0$
Use the following table to draw the graph.
|
$x$
|
$0$
|
$6$
|
|
$y$
|
$6$
|
$0$
|
Graph of the equation,
$x - y = 2 .......(ii)$
Putting $x = 0$ in equation $(ii)$ we get,
$\Rightarrow 0 - y = 2$
$\Rightarrow y = -2$
$\Rightarrow x = 0, y = -2$
Putting $y = 0$ in equation $(ii)$, we get,
$\Rightarrow x - 0 = 2$
$\Rightarrow x = 2$
$\Rightarrow x = 2, y = 0$
Use the following table to draw the graph.
|
$x$
|
$0$
|
$2$
|
|
$y$
|
$-2$
|
$0$
|
The two lines intersect at points$ P(4, 2).$
Hence $x = 4, y = 2$ is the solution.
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