Question
Solve graphically that the following system of equation has infinitely many solutions:
$2x + 3y = 6$
$4x + 6y = 12$
✓
Answer
So we have $2x + 3y = 6$ and $4x + 6y = 12.$
Now, $2x + 3y = 5$
$\text{x}=\frac{6-3\text{y}}{2}$
When $y = 0$ then,$ x = 3$ when $y = 2$ then, $x = 0$
Now, 4x + 6y = 12
$\text{x}=\frac{12-6\text{y}}{4}$
When $y = 0$, then $x = 3$ When $y = 2$, then $x = 0$
Thus, we have the following table giving points on the line $4x + 6y = 12$
Graph of the equation $2x + 3y = 6$ and $4x + 6y = 12$
Thus the graphs of the two equations are coincident. Hence, the system of equations has infinitely many solutions.
Now, $2x + 3y = 5$
$\text{x}=\frac{6-3\text{y}}{2}$
When $y = 0$ then,$ x = 3$ when $y = 2$ then, $x = 0$
|
$x$
|
$0$
|
$3$
|
|
$y$
|
$2$
|
$0$
|
$\text{x}=\frac{12-6\text{y}}{4}$
When $y = 0$, then $x = 3$ When $y = 2$, then $x = 0$
Thus, we have the following table giving points on the line $4x + 6y = 12$
|
$x$
|
$0$
|
$3$
|
|
$y$
|
$2$
|
$0$
|
Thus the graphs of the two equations are coincident. Hence, the system of equations has infinitely many solutions.
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