Provide a system of equations in slope-intercept form that has one solution. Using complete sentences, explain why this system has one solution.
If they have the same slope, then there are two possibilities. First say they have the same slope and different y intercepts. This means they are parallel lines and there is no intersection. The solution is the empty set or we say there is no solution.If the y intercept is the same, then the two equations represent the same line. In this case there is an infinite number of solutions.
No the only time that a system of equations would have no solutions is when the two equations have the same slope but different y-intercepts which would mean that they are parallel lines. However, if they have different slopes and different y-intercepts than the solution would be where the two lines intersect.
If the equations are in y= form, set the two equations equal to each other. Then solve for x. The x value that you get is the x coordinate of the intersection point. To find the y coordinate of the intersection point, plug the x you just got into either equation and simplify so that y= some number. There are other methods of solving a system of equations: matrices, substitution, elimination, and graphing, but the above method is my favorite!
x = y = 3
there is no linear equations that has no solution every problem has a solution
The pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.
x = 1 and y = 2
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.
The solution of a system of linear equations is a pair of values that make both of the equations true.
It is used for solving a system of linear equations where the number of equations equals the number of variables - and it is known that there is a unique solution.
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.
If a system has no solution, it means that the lines are parallel.