Several methods exist. For example: solve one equation for one variable, replace that variable in the other equation. (Two simultaneous equations will often have two variables each.)
The graphs of a system of two equations in two variables can determine the solutions to the system. If the graphs intersect at a single point, that point represents the unique solution. If the graphs are parallel and do not intersect, the system has no solution (inconsistent). If the graphs coincide, there are infinitely many solutions (dependent).
Yes, you can determine the nature of a system of two linear equations by analyzing their slopes and intercepts. If the lines represented by the equations have different slopes, the system has one solution (they intersect at a single point). If the lines have the same slope but different intercepts, there is no solution (the lines are parallel). If the lines have the same slope and the same intercept, there are infinitely many solutions (the lines coincide).
The graphs of the two equations have only one intersection point.
There is no special name. Two totally unrelated equations could have the same solution(s).
simultaneous equations
The graphs of a system of two equations in two variables can determine the solutions to the system. If the graphs intersect at a single point, that point represents the unique solution. If the graphs are parallel and do not intersect, the system has no solution (inconsistent). If the graphs coincide, there are infinitely many solutions (dependent).
Yes, you can determine the nature of a system of two linear equations by analyzing their slopes and intercepts. If the lines represented by the equations have different slopes, the system has one solution (they intersect at a single point). If the lines have the same slope but different intercepts, there is no solution (the lines are parallel). If the lines have the same slope and the same intercept, there are infinitely many solutions (the lines coincide).
equal equations.
The solution of a system of linear equations is a pair of values that make both of the equations true.
The two equations represent parallel lines.
The graphs of the two equations have only one intersection point.
If you graph the two functions defined by the two equations of the system, and their graphs are two parallel line, then the system has no solution (there is not a point of intersection).
The slopes (gradients) of the two equations are different.
There is no special name. Two totally unrelated equations could have the same solution(s).
Consistent equations are two or more equations that have the same solution.
simultaneous equations
If the graphs of the two equations in a system are the same, the system must have A. more than 1 solution. This is because the two equations represent the same line, meaning every point on that line is a solution to the system. Therefore, there are infinitely many solutions.