Question
Solve graphically that the following system of equation has infinitely many solutions:
3x + y = 8
6x + 2y = 16
✓
Answer
The given equations are,
3x + y = 8 .......(i)
6x + 2y = 16 ........(ii)
From (i), y = 8 - 3x .......(iii)
Putting x = 0 in (iii), we get y = 8
Putting x = 1 in (iii), we get y = 5
Putting x = 2 in (iii), we get y = 2
From (ii), $\text{y}=\frac{16-6\text{x}}{2}\ .....(\text{iv})$
Putting x = 1 in (iv), we get y = 5
Putting x = 2 in (iv), we get y = 2
Putting x = 3 in (iv), we get y = -1
When we polt these points on graph paper we observe that all then points on a line so the given system of equations has infinitaly many solutions.
3x + y = 8 .......(i)
6x + 2y = 16 ........(ii)
From (i), y = 8 - 3x .......(iii)
Putting x = 0 in (iii), we get y = 8
Putting x = 1 in (iii), we get y = 5
Putting x = 2 in (iii), we get y = 2
|
x
|
0
|
1
|
2
|
|
y
|
8
|
5
|
2
|
Putting x = 1 in (iv), we get y = 5
Putting x = 2 in (iv), we get y = 2
Putting x = 3 in (iv), we get y = -1
|
x
|
1
|
2
|
3
|
|
y
|
5
|
2
|
-1
|
When we polt these points on graph paper we observe that all then points on a line so the given system of equations has infinitaly many solutions.
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