Is a system consistent if it has infinitely many solutions?

A system of two linear equations can have one solution, an infinite number of solutions, or no solution. If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent .

When a system of equations has no solution?

A system of linear equations has no solution when the graphs are parallel. Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.

How do you know if two equations have no solution?

The coefficients are the numbers alongside the variables. The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.

What is the condition for no solution?

For no solution, Two lines have no solution, if these two lines are parallel to each other. The lines are parallel to each other means that the slopes of the lines are equal.

What is an equation that has no solution?

No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. Note that we have variables on both sides of the equation.

How many solutions does a system have?

One solution. A system of linear equations has one solution when the graphs intersect at a point. No solution. A system of linear equations has no solution when the graphs are parallel. Infinite solutions.

What does infinitely many solutions mean in math?

Infinitely Many Solutions. When an equation has infinitely many solutions, it means that if the variable was turned into a number, the equation would be correct or true, no matter which number or value is placed.

How do you calculate system of equations?

Solve by Multiplication Write one equation above the other. Multiply one or both equations until one of the variables of both terms have equal coefficients. Add or subtract the equations. Solve for the remaining term. Plug the term back into the equation to find the value of the first term. Check your answer.

How many solutions does the system?

A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line). This article reviews all three cases.

Is a system consistent if it has infinitely many solutions? A system of two linear equations can have one solution, an infinite number of solutions, or no solution. If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent .…