Question
Solve the following simultaneous equation graphically.
5x – 6y + 30 = 0; 5x + 4y – 20 = 0
5x – 6y + 30 = 0; 5x + 4y – 20 = 0
✓
Answer
The given simultaneous equations are
$5 x-6 y+30=0$
$\therefore \quad 6 y=5 x+30$
$\therefore \quad y=\frac{5 x+30}{6}$
$5 x+4 y-20=0$
$\therefore \quad 4 y=20-5 x$
$\therefore \quad y=\frac{20-5 x}{4}$
The two lines intersect at point (0, 5).
∴ x = 0 and y = 5 is the solution of the simultaneous equations 5x – 6y + 30 = 0 and 5x + 4y – 20 = 0.
$5 x-6 y+30=0$
$\therefore \quad 6 y=5 x+30$
$\therefore \quad y=\frac{5 x+30}{6}$
| x | 0 | -6 | 6 | 3 |
| y | 5 | 0 | 10 | 7.5 |
| (x, y) | (0, 5) | (-6, 0) | (6, 10) | (3, 7.5) |
$5 x+4 y-20=0$
$\therefore \quad 4 y=20-5 x$
$\therefore \quad y=\frac{20-5 x}{4}$
| x | 0 | 4 | -4 | 2 |
| y | 5 | 0 | 10 | 2.5 |
| (x, y) | (0, 5) | (4, 0) | (-4, 10) | (2, 2.5) |
The two lines intersect at point (0, 5).
∴ x = 0 and y = 5 is the solution of the simultaneous equations 5x – 6y + 30 = 0 and 5x + 4y – 20 = 0.
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