Question
Solve graphically that the following system of equation has infinitely many solutions:
x - 2y = 5
3x - 6y = 15
✓
Answer
We have,
x - 2y = 5
3x - 6y = 15
Now, x - 2y = 5
⇒ x = 2y + 5
When y = -1, we have,
x = 2(-1) + 5 = 3
When y= 0, we have,
x = 2 × 0 + 5 = 5
Thus, we have the following table giving points on the line x - 2y = 5
Now, 3x - 6y = 15
⇒ 3x = 15 + 6y
$\Rightarrow\text{x}=\frac{15+6\text{y}}{3}$
When y = -2, we have,
$\text{x}=\frac{15+6(-2)}{3}=1$
When y = -3, we havce,
$\text{x}=\frac{15+6(-3)}{3}=-1$
Thus, we have the following table giving points on the line 3x - 6y = 15
Graph of the given equations,
After plot all points observe that all points on a line so that system of equation has infinite many solution.
x - 2y = 5
3x - 6y = 15
Now, x - 2y = 5
⇒ x = 2y + 5
When y = -1, we have,
x = 2(-1) + 5 = 3
When y= 0, we have,
x = 2 × 0 + 5 = 5
Thus, we have the following table giving points on the line x - 2y = 5
|
x
|
3
|
5
|
|
y
|
1
|
0
|
⇒ 3x = 15 + 6y
$\Rightarrow\text{x}=\frac{15+6\text{y}}{3}$
When y = -2, we have,
$\text{x}=\frac{15+6(-2)}{3}=1$
When y = -3, we havce,
$\text{x}=\frac{15+6(-3)}{3}=-1$
Thus, we have the following table giving points on the line 3x - 6y = 15
|
x
|
1
|
-1
|
|
y
|
-2
|
-3
|
After plot all points observe that all points on a line so that system of equation has infinite many solution.
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