No. They can just as well have zero solutions, several solutions, or even infinitely many solutions.
So, take the case of two parallel lines, there is no solution at all. Now look at two equations that represent the same line, they have an infinite number of solutions. The solution is unique if and only if there is a single point of intersection. That point is the solution.
You take each equation individually and then, on a graph, show all the points whose coordinates satisfy the equation. The solution to the system of equations (if one exists) consists of the intersection of all the sets of points for each single equation.
All the lines meet at one point: a single solution. All the lines are the same: infinitely many solutions. At least one of the lines does not pass through the point of intersection of the others: no solution.
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.
Numbers are numbers, not questions or equations. They do not have solutions.
yes they do except for the one on your test that is worth he most marks
No. They can just as well have zero solutions, several solutions, or even infinitely many solutions.
A system of linear equations determines a line on the xy-plane. The solution to a linear set must satisfy all equations. The solution set is the intersection of x and y, and is either a line, a single point, or the empty set.
It is a trivial difference. If you multiply every term in the equation with rational numbers by the common multiple of all the rational numbers then you will have an equation with integers.
So, take the case of two parallel lines, there is no solution at all. Now look at two equations that represent the same line, they have an infinite number of solutions. The solution is unique if and only if there is a single point of intersection. That point is the solution.
That would be the "solution" to the set of equations.
An "inconsistent" set of equations. If they are all linear equations then the matrix of coefficients is singular.
You take each equation individually and then, on a graph, show all the points whose coordinates satisfy the equation. The solution to the system of equations (if one exists) consists of the intersection of all the sets of points for each single equation.
All the lines meet at one point: a single solution. All the lines are the same: infinitely many solutions. At least one of the lines does not pass through the point of intersection of the others: no solution.
Any solution to a system of linear equations must satisfy all te equations in that system. Otherwise it is a solution to AN equation but not to the system of equations.
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.