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 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.
The graphs of the two equations have only one intersection point.
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.
simultaneous equations
They will be a set of lines meeting at one point - the solution.
Provide a system of equations in slope-intercept form that has one solution. Using complete sentences, explain why this system has one solution.
It is a set of equations, which is also called a system of equations. There may be no solution, a single (unique) solution or more than one - including infinitely many.
Put the values that you find (as the solution) back into one (or more) of the original equations and evaluate them. If they remain true then the solution checks out. If one equation does not contain all the variables involved in the system, you may have to repeat with another of the original equations.
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
The slopes (gradients) of the two equations are different.
A system of linear equations that has at least one solution is called consistent.