Question
Solve the following simultaneous equation graphically.
2x + 3y = 12; x – y = 1
2x + 3y = 12; x – y = 1
✓
Answer
The given simultaneous equations are
$2 x+3 y=12$
$\therefore \quad 3 y=12-2 x$
$\therefore \quad y=\frac{12-2 x}{3}$
$x-y=1$
$\therefore \quad y=x-1$
The two lines interest at point (3,2).
∴ x = 3 and y = 2 is the solution of the simultaneous equations 2x + 3y = 12 and x – y = 1.
$2 x+3 y=12$
$\therefore \quad 3 y=12-2 x$
$\therefore \quad y=\frac{12-2 x}{3}$
| x | 0 | 6 | 3 | -3 |
| y | 4 | 0 | 2 | 6 |
| (x, y) | (0, 4) | (6, 0) | (3, 2) | (-3, 6) |
$x-y=1$
$\therefore \quad y=x-1$
| x | 0 | 2 | 4 | 5 |
| y | -1 | 1 | 3 | 4 |
| (x, y) | (0, -1) | (2, 1) | (4, 3) | (-4, 4) |
The two lines interest at point (3,2).
∴ x = 3 and y = 2 is the solution of the simultaneous equations 2x + 3y = 12 and x – y = 1.
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