Question
Solve the following system of linear equation graphically and shade the region between the two lines and x-axis:
2x + 3y = 12,
x - y = 1.
✓
Answer
The system of given equations is,
2x + 3y = 12
x - y = 1
Now, 2x + 3y = 12
⇒ 2x = 12 - 3y
When y = 2, we have,
$\text{x}=\frac{12-3\times2}{2}=3$
When y = 4, we have,
$\text{x}=\frac{12-3\times4}{2}=0$
Thus, we have the following table,
We have, x - y = 1
⇒ x = 1 + y
When y = 0, we have,
x = 1
When y = 1, we have,
x = 1 + 1 = 2
Thus, we have the following table,
Graph of the given system of equations.
Clearly, the two lines intersect at P(3, 2).
Hence, x = 3, y = 2 is the solution of the given system of equations.
2x + 3y = 12
x - y = 1
Now, 2x + 3y = 12
⇒ 2x = 12 - 3y
When y = 2, we have,
$\text{x}=\frac{12-3\times2}{2}=3$
When y = 4, we have,
$\text{x}=\frac{12-3\times4}{2}=0$
Thus, we have the following table,
|
x
|
0
|
3
|
|
y
|
4
|
2
|
⇒ x = 1 + y
When y = 0, we have,
x = 1
When y = 1, we have,
x = 1 + 1 = 2
Thus, we have the following table,
|
x
|
1
|
2
|
|
y
|
0
|
1
|
Clearly, the two lines intersect at P(3, 2).
Hence, x = 3, y = 2 is the solution of the given system of equations.
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