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Linear Equations in One Variable
An equation of one variable and of first order (i.e., its highest power is one) is called a Linear equation. Such an equation has only one solution. A solution is also called the 'root' of the given equation.An equation of one variable and of first ..
Question 8
Question: Solve the following equation: Answer: 2x-(1-2x) = 5-3(1+x) 2x-1+2x = 5-3-3x 4x+3x = 5-3+1 7x=3 ..
Second Method:
>-13x will be written as -10x - 3x] = 2x(3x - 5) - 1(3x - 5) = (3x - 5)(2x - 1) Resolve into factors: 7x 2 + 11x - 6 The product of 7h..
Worked Examples on Simultaneous Equations
Problems on Simultaneous Equations - If one number is thrice the other and their sum is 60, find the numbers. Let the numbers be x and y. x is 3 times y x = 3y (1) Sum of x and y is 60 x + y = 60 (2) Putting the value o..
Formula
>A number of two digits p and q in that order is 7 greater than the number formed by reversing the digits. The ten's digit is p and the unit's digit is q. Then the number is 10p + q. The number formed by reversing the digits = 10q + p (10p + q) - (10q + p) = 7 A man wa..
Surd
(ii) If 2 x + 2 = 128, find the value of x. (iii) Simplify: (iv) Simplify: (v) Show that (x p - q ) p + q (x q - r ) q + r (x r - s ) r + s = 1 (vi) 49 7 x = (343) 2 x - 5 find 'h..
Cartesian product of two sets
Let A and B be two non-empty sets, then the cartesian product of A and B denoted by A x B = {(a, b) | a A, b B..
1)
Graph the following: x > 2 and y < 3 The solution set of the system of linear simultaneous inequations is the set of all points (x, y) which satisfies the given set of inequations. In the above graph, the common area of the inequations (shaded area) represent..
Graph of Linear Equation in one variable
ax + b = 0 is a linear equation in one variable. Consider the equation 2x + 4 = 0 2x = -4 x = -2 Since this equation is independent of y, for all values of y, x = -2 Hence x = -2 is a line ..
Example 1:
Plot the graph of 2x+3y=..
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