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Tripti Rawat 5 years, 5 months ago
A non-aqueous solution is a solution in which water is not the solvent. Examples of non-aqueous solutions are solutions used in dry cleaning (a solution of ethene in the solvent dichloromethane).
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Sia ? 5 years, 5 months ago
Consider the following pair of linear equations in two variables,
- x – 2y = 0
- 3x + 4y = 20
The solution of this pair would be a pair (x, y). Let’s find the solution, geometrically. The tables for these equations are:
| x | 0 | 2 |
| y = (1/2)x | 0 | 1 |
| x | 0 | 4 |
| y = (20 – 3x)/4 | 5 | 2 |
Now, take a graph paper and plot the following points:
- A(0, 0)
- B(2, 1)
- P(0, 5)
- Q(4, 2)
Next, draw the lines AB and PQ as shown below.
From the figure above, you can see that the two lines intersect at the point Q (4, 2). Therefore, point Q lies on the lines represented by both the equations, x – 2y = 0 and 3x + 4y = 20. Hence, (4, 2) is the solution of this pair of equations in two variables. Let’s verify it algebraically:
- x – 2y = 4 – 2(2) = 4 – 4 = 0 = RHS
- 3x + 4y = 3(4) + 4(2) = 12 + 8 = 20 = RHS
Posted by Vansh Gupta 5 years, 5 months ago
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Tripti Rawat 5 years, 5 months ago
Using identity ---- a^3 - b^3= (a-b)(a^2+a×b+b^2),
= x {(1)^3 - (2×y)^3}
= x {1 - 2y} { (1)^2 + 1×2y + (2y)^2 }
= x {1 - 2y} { 1 + 2y + 4(y)^2 }
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Yogita Ingle 5 years, 5 months ago
Let us draw the graphs of both the equations. The tables for these equations are:
| x | 0 | 6 |
| y = (6 – x)/3 | 2 | 0 |
| x | 0 | 3 |
| y = (2x – 12)/3 | – 4 | – 2 |
Now, take a graph paper and plot the following points:
- A (0, 2)
- B (6, 0)
- P (0, – 4)
- Q (3, – 2)
Next, draw the lines AB and PQ as shown below.
From the figure above, you can see that the two lines intersect at the point B (6, 0). Therefore, x = 6 and y = 0 is the solution of this pair of equations in two variables. Hence, it is Consistent.
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