• ONLY x = 1 is a solution of the original equation! x = -2 cannot be a solution, because you can't take logs of negative numbers, so if you try to put x = -2 into the original logarithmic equation you would get . log 2 (-2 + 1) +log 2 (-2) = 1. Neither logarithm makes sense, so -2 can't be a solution.
  • Do you see the similarity between what happened now and what happened when we solved for a spherically symmetric solution to the wave equation? If there were really no charges or currents at the origin, there would not be spherical outgoing waves. The spherical waves must, of course, be produced by sources at the origin.
  • Figure 63: Solution of Poisson's equation in two dimensions with simple Dirichlet boundary conditions in the -direction.The solution is plotted versus at .The dotted curve (obscured) shows the analytic solution, whereas the open triangles show the finite difference solution for .
  • A system of equations refers to a number of equations with an equal number of variables. We will only look at the case of two linear equations in two unknowns. The situation gets much more complex as...
  • Solving Equations We begin with the basics, that is solving simple equations. The most impor-tant thing to remember when solving equations is that whatever you do to one side you need to also do to the other. We will use letters x, yand zto denote the things that we want to nd out. Take an example. Let xbe the cost of a meal in a particular ...
  • Many students assume that all equations have solutions. This article will use three examples to show that assumption is incorrect. Given the equation 5x - 2 + 3x = 3(x+4)-1 to solve, we will collect our like terms on the left hand side of the equal sign and distribute the 3 on the right hand side of the equal sign. 5x ...
  • No matter how many steps are in the original equation, you can work backwards and apply the inverse operations, in order, to arrive at the solution! You can solve two-step inequalities in exactly the same way. Just work backwards, using the inverse operations, to arrive at the solution.
  • Thus as a congruence this equation has a solution mod m for any m. That there is no Z-solution follows from Q(sqrt(-51)) having class number 2, which is rel. prime to 3, by the same kind of method used to find the Z-solutions to y^2 = x^3-2. $\endgroup$ – KConrad Nov 28 '10 at 7:19

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The following system of equations has no solution. \(\begin{array}{l} x-y=-2\\ \\x-y=1\end{array}\) How would you know? One way would be to try and solve the system, and see that you get an untrue statement. Another would be to realize that the first equation is saying that x–y is one number, while the second equation is saying that x–y has a different value. These can’t both be true.
Absolute Value Equations. Follow these steps to solve an absolute value equality which contains one absolute value: Isolate the absolute value on one side of the equation. Is the number on the other side of the equation negative? If you answered yes, then the equation has no solution. If you answered no, then go on to step 3.

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A system of two linear equations has no solution. The first equation is 3 x + y = −5. Select the second equation that would make this system have no solution.
Sometimes equations have no solution. This means that no matter what value is plugged in for the variable, you will ALWAYS get a contradiction. Watch this tutorial and learn what it takes for an equation to have no solution.

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How to know if an equation has Infinitely Many Solutions or No Solution? We look at these 2 special cases in this free math video tutorial by Mario's Math Tu...
2 days ago · As Example:, 8x 2 + 5x – 10 = 0 is a quadratic equation. Root of quadratic equation: Root of a quadratic equation ax 2 + bx + c = 0, is defined as real number α, if aα 2 + bα + c = 0. The zeroes of the quadratic polynomial and the roots of the quadratic equation ax 2 + bx + c = 0 are the same. Solution of a Quadratic Equation by different ...