Linear Equation With Infinite Solutions Math
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Y 2x 1.
Linear equation with infinite solutions math. Conditions for infinite solution. Subtracting 15 x from both sides. A 1 x b 1 y c 1 1 a 2 x b 2 y c 2 2 the given equations are consistent and dependent and have infinitely many solutions if and only if a 1 a 2 b 1 b 2 c 1 c 2 conditions for infinite solution. An equation can have infinitely many.
Thus suppose we have two equations in two variables as follows. This is the rarest case and only occurs when you have the same line consider for instance the two lines below y 2x 1 and 2y 4x 2. If a pair of the linear equations have unique or infinite solutions then the system of equation is said to be a consistent pair of linear equations. A system of linear equations has infinitely many solutions if the lines have the same slope and the same y intercept.
It is usually represented by the symbol. Show which of these possibilities is the case by successively transforming the given equation into simpler forms until an equivalent equation of the form x a a a or a b results where a and b are different numbers. The equation 2 x 3 x x 3 is an example of an equation that has an infinite number of solutions. 2 1 4 3 1 2 x 1 x 2 a 5 7.
Hence the given linear equation has infinite solutions or the number of solutions is infinite. Example of a system that has infinite solutions. Notice how the slope is the same and how the y intercept is the same. 2y 4x 2.
An infinite solution can be. Our x here marks the whole world which doesn t help us. If you simplify the equation using an infinite solutions formula or method you ll get both sides equal hence it is an infinite solution. Y 2x 1.
An infinite solution has both sides equal. For example 6x 2y 8 12x 4y 16. Infinite represents limitless or unboundedness. For example the following systems of linear equations will have infinitely many solutions.
Give examples of linear equations in one variable with one solution infinitely many solutions or no solutions. Consider the equation 15 x 9 24 x 9 9 x 126 solving we have 15 x 144 24 x 9 9 x 126 or 15 x 144 15 x 144. Let s see what happens when we solve. These two equations are really the same line.
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