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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
What is the situation when two linear inequalities have no common solution?
To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent).
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.
What is a system of equations that has at least one solution?
a linear equation
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.
What system of two linear equations in two variables that has exactly one solution?
An independent system has one solution.
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.
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
What do you call the graphs that intersect at exactly one point which gives solution of the system?
They are straight line graphs that work out the solutions of 2 equations or simultaneous equations
Can a system of two linear equations have exactly two solutions explain?
No, a system of two linear equations cannot have exactly two solutions. In a two-dimensional space, two linear equations can either intersect at one point (one solution), be parallel (no solutions), or be the same line (infinitely many solutions). Therefore, it is impossible for a system of two linear equations to have exactly two solutions.
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.
Two lines intersect how many solutions does the system of equations have?
When two lines intersect, the system of equations has exactly one solution. This solution corresponds to the point of intersection, where both equations are satisfied simultaneously. If the lines are parallel, there would be no solutions, and if they coincide, there would be infinitely many solutions.
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 the situation when two linear inequalities have no common solution?
To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent).
Is it possible to have a system of equations that has more than one solution?
Yes, a system of equations can have more than one solution if the equations represent the same line or plane in a geometric sense. In such cases, there are infinitely many solutions that satisfy all equations simultaneously. This typically occurs in systems of linear equations where the equations are dependent. Conversely, if the equations are independent, the system will either have a unique solution or no solution at all.
