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प्रश्न
Taking scale 2 cm = 1 unit, draw the graph of the following and find the solution set.
3x + 5y = 12
3x − 5y + 18 = 0
आलेख
बेरीज
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उत्तर
Step 1: Convert to slope-intercept form
Equation 1:
3x + 5y = 12
5y = −3x + 12
y = `−3/5x + 12/5`
Equation 2:
3x − 5y + 18 = 0
3x − 5y = − 18
−5y = −3x − 18
y = `3/5x + 18/5`
Step 2:
Tables for equation: y = `−3/5x + 12/5`
| Calculation | (x, y) |
| y = `−3/5 (−3) + 12/5 = (9 + 12)/5 = 21/5` | (−3, 4.2) |
| y = `−3/5(−1) + 12/5 = (3 + 12)/5 = 15/5` | (−1, 3) |
| y = `−3/5(0) + 12/5 = 12/5` | (0, 2.4) |
| y = `−3/5(3) + 12/5 = (−9 + 12)/5 = 3/5` | (3, 0.6) |
| y = `−3/5(5) + 12/5 = (−15 + 12)/5 = −3/5` | (5, −0.6) |
Tables for equation: y = `3/5x + 18/5`
| Calculation | (x, y) |
| y = `3/5(−3) + 18/5 = (−9 + 18)/5 = 9/5` | (−3, 1.8) |
| y = `3/5(−1) + 18/5 = (−3 + 18)/5 = 15/5` | (−1, 3) |
| y = `3/5(0) + 18/5 = 18/5` | (0, 3.6) |
| y = `3/5(2) + 18/5 = (6 + 18)/5 = 24/5` | (2, 4.8) |
| y = `3/5(3) + 18/5 = 9 + 18/5 = 27/5` | (3, 5.4) |
The two lines intersect at the point (−1,3).
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