Yes. The easiest case to see where this is true is in the case that the equations are all of degree = 1, which will yield one solution per variable.
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.
It means that there is no set of values for the variables such that all the linear equations are simultaneously true.
A.infinitely manyB.oneD.zero
1
False. There can either be zero, one, or infinite solutions to a system of two linear equations.
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 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.
It means that there is no set of values for the variables such that all the linear equations are simultaneously true.
A.infinitely manyB.oneD.zero
1
Yes.
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
A linear system is a set of equations where each equation is linear, meaning it involves variables raised to the power of 1. Solving a linear system involves finding values for the variables that satisfy all the equations simultaneously. This process is used to find solutions to equations with multiple variables by determining where the equations intersect or overlap.
False. There can either be zero, one, or infinite solutions to a system of two linear equations.
Yes, a system can, in fact, have exactly two solutions.
A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.
None, one or infinitely many.