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Linear equations in two variables
An equation whose graph is a straight line is called a linear equation. (linear means straight). An equation of degree one is linear.An equation whose graph is a straight line is called a linear equation. (linear means straight). An equation of degree one is linear. A linear equ..
Linear equations in two variables with examples
Linear equations in two variables - An equation whose graph is a straight line is called a linear equation. (linear means straight). An equation of degree one is linear.An equation whose graph is a straight line is called a linear equation. (linear means straight). An ..
(ii) Cartesian graph
{(1, 1), (2, 2). (3, 3), (4, 4)}..
2)
Graph the following: Consider the equations, ..
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 parallel to the y-axis at x = -2. Consider the equ..
Example 1:
Plot the graph of 2x+3y=..
Example 4:
Plot the graph of 5x-2y=5. Use the graph to find the area between the line and the axe..
Following are the test for Functions
(a) (i) The relation should be one-one or many-one, and (ii) Every first element is mapped which means that every pre-image should have an image. (b) For graphs: Draw a line parallel to the y-axis. If it cuts the graph only in one point, then the graph represents a fu..
Example:
Find at least 3 sets of values for the variables satisfying the equation. 2x+y=5 Express y in terms of x. y=5-2x Select three values of x, find corresponding values of y. x=0, y=5-(2x0)=5 x=1, y=5-(2x1)=3 x=-1, y=5-(-2)=7 Draw the x and y - axe..
Linear Inequations Summary
Linear Inequations Summary - A half-plane in the x-y plane is called a closed half-plane if the points on the line separating the half-planes are also included in the half-plane. A half-plane in the x-y plane is called a closed half-plane if the points on the line separating the half-planes are als..
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