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, $x - 2y = 5$
$\Rightarrow x = 2y + 5$
When $y = -1$, we have,
$x = 2(-1) + 5 = 3$
When $y= 0$, we have,
$x = 2 \times 0 + 5 = 5$
Thus, we have the following table giving points on the line $x - 2y = 5$
Now, $3x - 6y = 15$
$\Rightarrow 3x = 15 + 6y$
$\Rightarrow\text{x}=\frac{15+6\text{y}}{3}$
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, $x - 2y = 5$
$\Rightarrow x = 2y + 5$
When $y = -1$, we have,
$x = 2(-1) + 5 = 3$
When $y= 0$, we have,
$x = 2 \times 0 + 5 = 5$
Thus, we have the following table giving points on the line $x - 2y = 5$
|
$x$
|
$3$
|
$5$
|
|
$y$
|
$1$
|
$0$
|
$\Rightarrow 3x = 15 + 6y$
$\Rightarrow\text{x}=\frac{15+6\text{y}}{3}$
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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