A system of linear equations can only have:
no solution,
one solution, or
infinitely many solutions.
if you can fart out of your chin then you know your headin in the right direction
Because linear lines can't intersect in two seperate places. They either intersect at one specific coordinate, or the lines are on top of each other and they intersect at every point.
In simple terms all that it means that there are more solutions than you can count!If the equations are all linear, some possibilities are given below (some are equivalent statements):there are fewer equations than variablesthe matrix of coefficients is singularthe matrix of coefficients cannot be invertedone of the equations is a linear combination of the others
Yes.
Two dependent linear equations are effectively the same equation - with their coefficients scaled up or down.
No, a system of two linear equations cannot have exactly two solutions. In a two-dimensional space, two linear equations can either intersect at one point (one solution), be parallel (no solutions), or be the same line (infinitely many solutions). Therefore, it is impossible for a system of two linear equations to have exactly two solutions.
if you can fart out of your chin then you know your headin in the right direction
False. There can either be zero, one, or infinite solutions to a system of two linear equations.
A system of linear equations cannot have two distinct solutions if it is consistent and defined in a Euclidean space. If two linear equations intersect at a single point, they have one solution; if they are parallel, they have no solutions. However, if the equations are dependent, meaning one equation is a multiple of the other, they represent the same line and thus have infinitely many solutions, not just two. Therefore, in standard scenarios, a system of linear equations can either have one solution, no solutions, or infinitely many solutions, but not exactly two.
Yes, a system can, in fact, have exactly two solutions.
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.
No. At least, it can't have EXACTLY 3 solutions, if that's what you mean. A system of two linear equations in two variables can have:No solutionOne solutionAn infinite number of solutions
Linear equations with one, zero, or infinite solutions. Fill in the blanks to form a linear equation with infinitely many solutions.
They are called simultaneous equations.
Because linear lines can't intersect in two seperate places. They either intersect at one specific coordinate, or the lines are on top of each other and they intersect at every point.
A system of two linear equations in two unknowns can have three possible types of solutions: exactly one solution (when the lines intersect at a single point), no solutions (when the lines are parallel and never intersect), or infinitely many solutions (when the two equations represent the same line). Thus, there are three potential outcomes for such a system.
Equations cannot be ordered.