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A system of equations with exactly one solution?
A system of equations with exactly one solution intersects at a singular point, and none of the equations in the system (if lines) are parallel.
A system of two linear equations has exactly one solution if?
The slopes (gradients) of the two equations are different.
If a system of linear equations has exactly one solution then the two lines are what?
perpendicular
How many solutions is it possible for a system of linear equations to have?
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
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.
A system of linear equations that has soluton is?
A system of linear equations that has at least one solution is called consistent.
A system of equations with exactly one solution?
A system of equations with exactly one solution intersects at a singular point, and none of the equations in the system (if lines) are parallel.
If a system of equations is independent how many soultions will it have?
A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.
Translate this word problem as a system of equations and then solve using substitution?
A system of equations is two or more equations that share at least one variable. Once you have determined your equations, solve for one of the variables and substitute in that solution to the other equation.
How do you know if a system has one solution?
If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.
System of equations in slope-intercept form that has one solution Using complete sentences explain why this system has one solution?
Provide a system of equations in slope-intercept form that has one solution. Using complete sentences, explain why this system has one solution.
What is consistent system with independent equations?
A consistent system with independent equations is one in which there is at least one solution, and the equations do not overlap in their constraints, meaning that no equation can be derived from another. In such a system, the equations represent different planes (or lines in two dimensions), and they intersect at one unique point (in the case of two variables) or along a line (for three variables). This unique intersection indicates that the system has a single solution that satisfies all equations simultaneously.
What does the solution represent when a system of equations has a single solution?
The graphs of the two equations have only one intersection point.
What system of two linear equations in two variables that has exactly one solution?
An independent system has one solution.
When does a system of linear equations in two variables have a unique or one solution?
simultaneous equations
Why a system of linear equations cannot have exactly two solutions?
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
How will a system of equations that has one solution be graphed?
They will be a set of lines meeting at one point - the solution.
