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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