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Q: When you solve equation describe how you know when there will be a infinite solutions?

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Such an equation has an infinite set of solutions. You can solve the equation for one variable, in terms of the other. Then, by replacing different values for one of the variables, you can get different solutions.

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No. There is not enough information in the equation x + 2y = 2, by itself, to solve it. There are an infinite number of solutions. A second equation, or information to allow a second equation to be derived, must be given to find a solution.

It is not appropriate to talk about "the" three solutions for this equations; the equation describes a straight line, and has an infinite number of solutions. Solve the equation for "y", substitute any value for "x", and calculate the corresponding value for "y", to get one opf these solutions.

You cannot solve one equation in two unknowns. The given equation defines a line in the 2-dimensional plane and every point on the line is a solution. There are, therefore, an infinite number of solutions.

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A linear equation in two variables will give an infinite number of solutions. These will comprise the coordinates of points along a straight line in 2-dimensional space.

Yes, that is often possible. It depends on the equation, of course - some equations have no solutions.

It very much depends on the equation. The procedure for solving an equation with just one variable is so very different from the procedure for finding solutions to non-linear equations in several variables.

Ya can't. Ya got two unknowns there. To solve for two unknowns, ya gotta have two equations. Widout anudder equation, ya got a infinite number of solutions.

The question contains an algebraic expression but, since there is no equality sign, there is no equation to solve.

There are many kinds of differential equations and their solutions require different methods.

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