Question
Solve the following system of equations graphically:
$3x + 2y = 4,$
$2x - 3y = 7$
$3x + 2y = 4,$
$2x - 3y = 7$
✓
Answer
On a graph paper, draw a horizontal line $X'OX$ and a vertical line $YOY$' representing the x-axis and y-axis, respectively.
Graph of $3x + 2y = 4:$
$3x + 2y = 4$
$\Rightarrow\text{y}=\frac{4-\text{3x}}{2}$
Thus we have the following table for $3x + 2y = 4$
Plot the points $A(0,2), B(2,-1)$ and $C(-2,5)$ on the graph paper.
Join $A B$ and $A C$ to get the graph line $B C$.
Extend it on both ways.
Thus, the line $B C$ is the graph of $3 x+2 y=4$.
Graph of $2 x-3 y=7$ :
$\Rightarrow y=\frac{2 x-7}{3}$
Thus, we have the following table for $2 x-3 y=7$ is
Now, on the same graph paper plot the points $P(-1,-3)$ and $Q(5,1)$. The point $B(2,-1)$ has already been plotted. Join $PB$ and $QB$ and extend it on both ways.
Thus, line $P Q$ is the graph of $2 x-3 y=7$.
The two graph lines intersect at $B(2, -1).$
$\therefore x = 2, y = -1$ is the solution of the given system of equations.
Graph of $3x + 2y = 4:$
$3x + 2y = 4$
$\Rightarrow\text{y}=\frac{4-\text{3x}}{2}$
Thus we have the following table for $3x + 2y = 4$
|
$x:$
|
$0$ |
$2$
|
$-2$
|
|
$y:$
|
$2$
|
$-1$
|
$5$
|
Join $A B$ and $A C$ to get the graph line $B C$.
Extend it on both ways.
Thus, the line $B C$ is the graph of $3 x+2 y=4$.
Graph of $2 x-3 y=7$ :
$\Rightarrow y=\frac{2 x-7}{3}$
Thus, we have the following table for $2 x-3 y=7$ is
|
$x:$
|
$2$
|
$-1$
|
$5$
|
|
$y:$
|
$-1$
|
$-3$
|
$1$
|
Thus, line $P Q$ is the graph of $2 x-3 y=7$.
The two graph lines intersect at $B(2, -1).$
$\therefore x = 2, y = -1$ is the solution of the given system of equations.
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