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This is an interesting problem.
But first, let us define what are the three possible cases :
A system of linear equations : a system of equation is when you have two equations with the same unknown variables, that you need to solve both together. Example : "x+y = - 7 AND x + y = - 4" are two equations that form a system of equation.
Plus they are linear, a linear equation is simply an equation of the form : y = ax + b where a and b are real numbers.
Here for example x + y = - 7 is a linear equation. Because y = 1 × x - 7
where a = 1 and b = - 7.
Consistent Dependent : A system of equation is consistent Dependant when it has an infinite number of solutions.
<h2><u><em>When this is the case, the graphs of the lines in the system are the same, meaning the equations in the system represent the same line. </em></u></h2><h2 />Consistent Independent : A system of equation is consistent Dependant when it has exactly one solution.
<h2><em><u>When this is the case, the graphs of the lines in the system cross at exactly one point. </u></em></h2><h2 />Inconsistent : A system of equation is Inconsistent if it haas no solutions.
<h2><em><u>When this is the case, the graphs of the lines in the system do not intersect, meaning they are parallel. </u></em></h2><h2 />Now, with those definitions above, we can work on our problem :
1. x + y = - 7 and x + y = - 4
Look at the picture attached the lines are parallel to each other so here the answer is Inconsistent
2. Same line : consistent dependent
3. Parallel Lines : Inconsistent
4. Lines cross at exactly one point :Consistent Independent
5. Lines cross at exactly one point : Consistent Independent.
You can see the graph of each systems in the pictures attached below.
Good luck, you will succeed :)
