Question
Determine, by drawing graphs, whether the following system of linear equations has a unique solution or not:
$2y = 4x - 6, 2x = y + 3.$
$2y = 4x - 6, 2x = y + 3.$
✓
Answer
The given equations are,
$2y = 4x - 6 ........(i)$
$2x = y + 3 ..........(ii)$
From (i), $\text{y}=\frac{4\text{x}-6}{2}\ .....(\text{iii})$
When $x = 0, y = -3$
$x = 1, y = -1$
$x = 2, y = 1$
P lot these points $A(0, -3), B(1, -1)$ and $C(2, 1)$ on graph paper and join then,
From $(ii), y = 2x - 3 ......(iv)$
When $x = 0, y = -3$
$x = 1, y = -1$
$x = 2, y = 1$
P lot these points $P(0, -3), Q(1, -1)$ and $R(2, 1)$ on graph paper and join then.
We observe that points $A, B, C$ and $P, Q, R$ on same line so the syatem of equation has infinitaly many solutions.
$2y = 4x - 6 ........(i)$
$2x = y + 3 ..........(ii)$
From (i), $\text{y}=\frac{4\text{x}-6}{2}\ .....(\text{iii})$
When $x = 0, y = -3$
$x = 1, y = -1$
$x = 2, y = 1$
P lot these points $A(0, -3), B(1, -1)$ and $C(2, 1)$ on graph paper and join then,
From $(ii), y = 2x - 3 ......(iv)$
When $x = 0, y = -3$
$x = 1, y = -1$
$x = 2, y = 1$
P lot these points $P(0, -3), Q(1, -1)$ and $R(2, 1)$ on graph paper and join then.
We observe that points $A, B, C$ and $P, Q, R$ on same line so the syatem of equation has infinitaly many solutions.
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