An independent system of equations has exactly one solution (x,y) . An inconsistent system has no solution, and a dependent system has an infinite number of solutions.Consequently, how many solutions does this system have?
Systems of linear equations can only have 0, 1, or an infinite number of solutions. These two lines cannot intersect twice. The correct answer is that the system has one solution.
Also Know, how do you know if a system has no solution? If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
Hereof, how do you find the unique solution of a system?
Condition for Unique Solution to Linear Equations A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point. i.e., if the two lines are neither parallel nor coincident.
How do you know if an equation has one solution no solution or infinitely many solutions?
If the equation ends with a false statement (ex: 0=3) then you know that there's no solution. If the equation ends with a true statement (ex: 2=2) then you know that there's infinitely many solutions or all real numbers. Let's see an example of both of these.
What is a consistent system of equations?
In mathematics and in particularly in algebra, a linear or nonlinear system of equations is called as consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, that when substituted into each of the equations makes each equation hold true as an identity.How do you solve system of equations?
Here's how it goes: - Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for y:
- Step 2: Substitute that equation into the other equation, and solve for x.
- Step 3: Substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.
What is the solution to the system?
The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. In this example, the ordered pair (4,7) is the solution to the system of linear equations.What is the definition of solution of an equation?
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true. For equations having one unknown, raised to a single power, two fundamental rules of algebra, including the additive property and the multiplicative property, are used to determine its solutions.What is no solution on a graph?
If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations. If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.How can a system of equations have infinite solutions?
When we graph systems of equations, the intersection of the lines is the solution. If a system has infinitely many solutions, then the lines overlap at every point. In other words, they're the same exact line! This means that any point on the line is a solution to the system.What does it mean if two equations have no solution?
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. Note that we have variables on both sides of the equation.What is a unique solution?
A system has a unique solution when it is consistent and the number of variables is equal to the number of nonzero rows. If the rref of the matrix for the system is , the solution is the single point ( 2, 1, 3 ) or x=2, y=1, z=3.What makes a solution unique?
If 2 equations are in fact the same such as x - y = 1,5 x - 5y = 5 then any point lying on that line is a solution such x = 3, y = 2 or x = 1,000 y = 999 and there is no unique solution. If one equation is a linear combination of two others then there is no unique solution.What is no solution?
The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation. This is because there is truly no solution—there are no values for x that will make the equation 12 + 2x – 8 = 7x + 5 – 5x true.What does it mean when determinant is zero?
If the determinant of a square matrix n×n A is zero, then A is not invertible. [When the determinant of a matrix is nonzero, the linear system it represents is linearly independent.] When the determinant of a matrix is zero, its rows are linearly dependent vectors, and its columns are linearly dependent vectors. 
