Let 22*41 = 13*a + b where a and b are integers and 0<=b<13
[b is the remainder when 22*41 is divided by 13.]
Suppose there are two solutions. That is
22*41 = 13*a + b and 22*41 = 13*c + d
13*a + b = 13*c + d
so that 13*(a - c) = (d - b)
This implies that a - c = 0 or the LHS divides the RHS.
But RHS = d - b < 13 so LHS cannot divide RHS.
Therefore a - c = 0 ie a = c.
Then LHS = 0 so RHS = 0 => d - b = 0.
That is a = c and b = d so that 13*a + b = 13*c + d ie the solution is unique.
Since 13 is prime, we can simplify the question to
22*41(mod 13) = 22(mod13)*41(mod13) = 9*2(mod 13) = 18(mod13) = 5.
A single equation is several unknowns will rarely have a unique solution. A system of n equations in n unknown variables may have a unique solution.
Radial solutions are unique linear and non-linear formula equations used in math to explain the Laplacian equation. To calculate problems, scientist must determine the function based on the variable provided in the equation.
Yes, there is a unique solution.
It is a linear equation in the two variables x and y. A single linear equation in two variables cannot be solved for a unique pair of values of x and y. The equation is that of a straight line and any point on the line satisfies the equation.
row reduce the matrix in question and see if it has any free variables. if it does then it has many solution's. If not then it only has one unique solution. which is of course the trivial solution (0)
No. The equation describes a straight line and the coordinates of any one of the infinitely many points on the line is a solution.
A single equation is several unknowns will rarely have a unique solution. A system of n equations in n unknown variables may have a unique solution.
A solution to an linear equation cx + d = f is in the form x = a for some a, we call a the solution (a might not be unique). Rewrite your sentence: x = 8, 8 is unique. So how many solution does it have?
The equations are consistent and dependent with infinite solution if and only if a1 / a2 = b1 / b2 = c1 / c2.
Nobody can help you find a solution until you get another equation to go along with this one. Your equation has two variables in it ... 'x' and 'y' ... so it has no unique solution all by itself.
No you can't. There is no unique solution for 'x' and 'y'. The equation describes a parabola, and every point on the parabola satisfies the equation.
False, think of each linear equation as the graph of the line. Then the unique solution (one solution) would be the intersection of the two lines.
There is no such pair. The solution to equation 1 and equation 2 is x = 1, y = 1. The solution to equation 2 and equation 3 is x = 1, y = 1. And the solution to equation 1 and equation 3 is any point on the line 3x + 2y = 5 - an infinite number of solutions. The fact that the determinant for equations 1 and 3 is zero (or that they are not independent) does not mean that there is no solution. It means that there is no UNIQUE solution. In this particular case, the two equations are equivalent and so have an infinite number of solutions.
Radial solutions are unique linear and non-linear formula equations used in math to explain the Laplacian equation. To calculate problems, scientist must determine the function based on the variable provided in the equation.
It is not possible to tell. The lines could intersect, in pairs, at several different points giving no solution. A much less likely outcome is that they all intersect at a single point: the unique solution to the system.
x = 3, y = 9 is one solution from infinite number of solutions.to find another solution just choose any number for x, substitue it in the equation, for example if x = 1, y= 4 * 1 - 3 = 1, so 1 and 1 is another solution for y = 4 x - 3In this question there is only one equation which contains two variables, so there is no unique solution.we need other independent equation contains the variables x and y then we can solve these equations simultaneously, i.e. we can find finite number of solution (its one solution in linear equations)
a1/a2 is not equal to b1/b2