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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