Question
Solve graphically the following system of linear equation. Also find the coordinates of the points where the lines meet axis of y.
3x + 2y = 12
5x - 2y = 4
✓
Answer
We have,
3x + 2y = 12
5x - 2y = 4
Now, 3x + 2y = 12
⇒ 3x = 12 - 2y
$\Rightarrow\text{x}=\frac{12-2\text{y}}{3}$
When y = 3, we have,
$\text{x}=\frac{12-2\times3}{3}=2$
When y = -3, we have,
$\text{x}=\frac{12-2\times(-3)}{3}=6$
Thus, we have the following table giving points on the line 3x + 2y = 12
Now, 5x - 2y = 4
⇒ 5x = 4 + 2y
$\Rightarrow\text{x}=\frac{4+2\text{y}}{5}$
When y = 3, we have,
$\text{x}=\frac{4+2\times3}{5}=2$
When y = -7, we have,
$\text{x}=\frac{4+2\times(-7)}{5}=-2$
Thus, we have the following table points on the line 5x + 2y = 4
Graph of the given equations,
Clearly, two intersect at P(2, 3).
Hence, x = 2, y = 3 is the solution of the given system of equations.
We also observe that lines represented by 3x + 2y = 12 and 5x - 2y = 4 meet y-axis at A(0, 6) and B(0, -2) respectively.
3x + 2y = 12
5x - 2y = 4
Now, 3x + 2y = 12
⇒ 3x = 12 - 2y
$\Rightarrow\text{x}=\frac{12-2\text{y}}{3}$
When y = 3, we have,
$\text{x}=\frac{12-2\times3}{3}=2$
When y = -3, we have,
$\text{x}=\frac{12-2\times(-3)}{3}=6$
Thus, we have the following table giving points on the line 3x + 2y = 12
|
x
|
2 | 6 |
|
y
|
3 | -3 |
⇒ 5x = 4 + 2y
$\Rightarrow\text{x}=\frac{4+2\text{y}}{5}$
When y = 3, we have,
$\text{x}=\frac{4+2\times3}{5}=2$
When y = -7, we have,
$\text{x}=\frac{4+2\times(-7)}{5}=-2$
Thus, we have the following table points on the line 5x + 2y = 4
|
x
|
2
|
-2 |
|
y
|
3 | -7 |
Clearly, two intersect at P(2, 3).
Hence, x = 2, y = 3 is the solution of the given system of equations.
We also observe that lines represented by 3x + 2y = 12 and 5x - 2y = 4 meet y-axis at A(0, 6) and B(0, -2) respectively.
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