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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