No. The graph of each linear equation is a straight line, and
two or more lines can't all intersect at more than one point.
* * * * *
Unless all the lines are, in fact, the same line. In that case each point on the line is a solution. That is, there are infinitely many solutions.
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
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
If the equations are linear, they may have no common solutions, one common solutions, or infinitely many solutions. Graphically, in the simplest case you have two straight lines; these can be parallel, intersect in a same point, or actually be the same line. If the equations are non-linear, they may have any amount of solutions. For example, two different intersecting ellipses may intersect in up to four points.
2
False. There can either be zero, one, or infinite solutions to a system of two linear equations.
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
Yes, a system can, in fact, have exactly two solutions.
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
A.infinitely manyB.oneD.zero
Yes.
They are a set of equations in two unknowns such that any term containing can contain at most one of the unknowns to the power 1. A system of linear equations can have no solutions, one solution or an infinite number of solutions.
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.
None, one or infinitely many.
If a system of linear equations has infinitely many solutions, it means that the two lines represented by the equations are coincident, meaning they lie on top of each other. This occurs when both equations represent the same line, indicating they have the same slope and y-intercept. As a result, any point on the line is a solution to the system.
There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.