Question
Solve the following system of equations graphically:
2x + 3y = 2,
x - 2y = 8
2x + 3y = 2,
x - 2y = 8
✓
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 2x + 3y = 2:
$\text{y}=\frac{2(1-\text{x})}{3}$
Putting x = 1, we get y = 0
Putting x = -2, we get y = 2
Putting x = 4, we get y = -2
$\therefore$ Table for 2x + 3y = 2 is
Plot the points A(1, 0), B(-2, 2) and C(4, -2) on the graph paper.
Join AB and AC to get the graph line BC.
Extend it on both ways.
Thus, the line BC is the graph of x + 3y = 2.
Graph of x - 2y = 8:
$\text{y}=\frac{\text{x}-8}{2}$
Putting x = 2, we get y = -3
Putting x = 4, we get y = -2
Putting x = 0, we get y = -4
Table for x - 2y = 8 is
Now, on the same graph paper plot the points P(0, -4) and Q(2, -3). The point C(4, -2) has already been plotted.
Join PQ and QC and extend it on both ways.
Thus, line PC is the graph of x - 2y = 8.
The two graph lines intersect at C(4, -2).
$\therefore$ x = 4, y = -2 is the solution of the given system of equations.
Graph of 2x + 3y = 2:
$\text{y}=\frac{2(1-\text{x})}{3}$
Putting x = 1, we get y = 0
Putting x = -2, we get y = 2
Putting x = 4, we get y = -2
$\therefore$ Table for 2x + 3y = 2 is
|
x:
|
1
|
-2
|
4
|
|
y:
|
0
|
2
|
-2
|
Join AB and AC to get the graph line BC.
Extend it on both ways.
Thus, the line BC is the graph of x + 3y = 2.
Graph of x - 2y = 8:
$\text{y}=\frac{\text{x}-8}{2}$
Putting x = 2, we get y = -3
Putting x = 4, we get y = -2
Putting x = 0, we get y = -4
Table for x - 2y = 8 is
|
x:
|
2
|
4
|
0
|
|
y:
|
-3
|
-2
|
-4
|
Join PQ and QC and extend it on both ways.
Thus, line PC is the graph of x - 2y = 8.
The two graph lines intersect at C(4, -2).
$\therefore$ x = 4, y = -2 is the solution of the given system of equations.
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