0
What else can I help you with?
It is impossible for a system of two linear equations to have exactly one solution. True or False?
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.
When the equation in a linear system have different slopes then the system has what kind of solution?
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.
What is cramer rule?
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
What is a unique solution in linear equations?
This is the case when there is only one set of values for each of the variables that satisfies the system of linear equations. It requires the matrix of coefficients. A to be invertible. If the system of equations is y = Ax then the unique solution is x = A-1y.
What is IVP in differential equations?
Initial Value Problem. A differential equation, coupled with enough initial conditions for there to be a unique solution. Example: y'' - 6y = exp(x) ; y'(0) = y(0) = 0
It is impossible for a system of two linear equations to have exactly one solution. True or False?
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.
How would you know if a linear equation has one solution?
A linear equation has one solution if its graph represents a straight line that intersects the coordinate plane at a single point. This occurs when the equation is in the form (y = mx + b), where (m) (the slope) is not equal to zero. Additionally, for a system of linear equations, if the equations represent lines with different slopes, they will intersect at exactly one point, indicating a unique solution.
How many solutions does x equals 8have?
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?
What is radial solution in mathematics?
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.
When will an equation have one solution no solution and infinitely many solutions?
An equation will have one solution when it represents a line that intersects with another line at a single point, indicating a unique solution. It will have no solution if the lines are parallel, meaning they never intersect. An equation has infinitely many solutions when it represents the same line, where every point on the line is a solution. These scenarios typically apply to linear equations in two variables.
Can linear equations have more than one solutions?
No, a linear equation in two variables typically has one unique solution, which represents the intersection point of two lines on a graph. However, if the equation represents the same line (as in infinitely many solutions) or if it is inconsistent (no solutions), then the type of solutions can vary. In general, a single linear equation corresponds to either one solution, no solutions, or infinitely many solutions when considering the same line.
Unique solution of linear solution in math?
a1/a2 is not equal to b1/b2
What does a air of linear equations having a unique solution represent graphically?
Presumably the question concerned a PAIR of linear equations! The answer is two straight lines intersecting at the point whose coordinates are the unique solution.
What is the significance of the boundary condition in the context of solving differential equations?
The boundary condition is important in solving differential equations because it provides additional information that helps determine the specific solution to the equation. It helps to define the behavior of the solution at the boundaries of the domain, ensuring that the solution is unique and accurate.
When the equation in a linear system have different slopes then the system has what kind of solution?
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.
What is a one solution in math?
In mathematics, a "one solution" refers to a situation where a mathematical equation or problem has exactly one unique solution. This means that there is a specific value or set of values that satisfies the equation without ambiguity. For example, the equation (x + 2 = 5) has the one solution (x = 3). Such situations often arise in linear equations, where the graph represents a straight line intersecting the axis at a single point.
What is cramer rule?
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
