In order for a system to have infinitely many solutions, it must contain an equation that could be solved by any set of variables. In simple terms, a two-variable system can only be solved through two distinct equations; however, if one of these equations becomes meaningless, or could be solved by any set of variables, the other equation becomes meaningless as well because any value of y could match a given value of x. In terms of linear algebra, or any set or matrices meant to represent a system, infinitely many solutions occur due to an all 0 row. After the system is reduced to row echelon form, an all 0 row indicates that all coefficients in a given equation are equal to 0, so it does not matter what the variables are. This means that the number of equations no longer equals the number of variables and it becomes impossible to solve through cancellation and back-substitution.
A system of linear inequalities give you a set of answers that could work. In day to day lives we actually use linear inequalities all the time. We are given questions and problems where we search for a number of possible solutions.
if you can, you could always search a online calculator and use that.
A linear system just means it's a line. A solution is just a point that is on that line. It means that the two coordinates of the point solve the equation that makes the line. Alternatively, it could mean there are 2 (or more) lines and the point is where they intersect; meaning its coordinates solve both (or all) equations that make the lines.
"Linear" equations are simply those where the highest power of any variable is 1 (one). There could be 2 variables in which case it is a straight line, or there might be three in which case it is a flat plane, or there might be a million in which case we don't know what it actually looks like.
It depends on the equation. It could have one, it could have an infinite number.
In order for a system to have infinitely many solutions, it must contain an equation that could be solved by any set of variables. In simple terms, a two-variable system can only be solved through two distinct equations; however, if one of these equations becomes meaningless, or could be solved by any set of variables, the other equation becomes meaningless as well because any value of y could match a given value of x. In terms of linear algebra, or any set or matrices meant to represent a system, infinitely many solutions occur due to an all 0 row. After the system is reduced to row echelon form, an all 0 row indicates that all coefficients in a given equation are equal to 0, so it does not matter what the variables are. This means that the number of equations no longer equals the number of variables and it becomes impossible to solve through cancellation and back-substitution.
A system of linear inequalities give you a set of answers that could work. In day to day lives we actually use linear inequalities all the time. We are given questions and problems where we search for a number of possible solutions.
if you can, you could always search a online calculator and use that.
If it is a linear system, then it could have either 1 solution, no solutions, or infinite solutions. To understand this, think of two lines (consider a plane which is just 2 dimensional - this represents 2 variables and 2 equations, but the idea can be extended to more dimensions).If the 2 lines intersect at a point, then that point represents a solution. If the lines are parallel, then they never intersect, and there is no solution. If the equations are such that they are just different ways of describing the same line, then they intersect at every point, so there are infinite solutions. If you have more than 2 lines then maybe some of them will intersect, but this is not a solution for the whole system. If all lines intersect at a single point, then that is the single solution for the whole system.If you have equations that describe something other than a straight line, then it's possible that they may intersect in more than one point.
A linear system just means it's a line. A solution is just a point that is on that line. It means that the two coordinates of the point solve the equation that makes the line. Alternatively, it could mean there are 2 (or more) lines and the point is where they intersect; meaning its coordinates solve both (or all) equations that make the lines.
"Linear" equations are simply those where the highest power of any variable is 1 (one). There could be 2 variables in which case it is a straight line, or there might be three in which case it is a flat plane, or there might be a million in which case we don't know what it actually looks like.
There is no specific name. It could be a linear or more complicated polynomial equations, it could be trigonometric, exponential or any one of many other types. It could be a combination of these
Babylonians used advance math, but not completely advanced. While they could solve linear equations and used Pythagorean triples, they did not use the number zero and occasionally their geometry was incorrect.
Yes
No. There could be no solution - no values for x, y, and z so that the 3 equations are true.
A linear equation corresponds to a line, and a linear inequality corresponds to a region bounded by a line. Consider the equation y = x-5. This could be graphed as a line going through (0,-5), (1,-4), (2,-3), and so on. The inequality y > x-5 would be the region above that line.