Why does a linear equation in two variables have infinite solutions?
Consider the equation ax+by=c. Thus, for every solution of this linear diophantine equation of two variables, there exists another unique solution. Hence, there is an infinite number of solutions to this equation.
Do all linear equations in two variables have infinite solutions?
For linear equations in two variables, inconsistent systems have no solution, while dependent systems have infinitely many solutions.
What makes a linear equation infinite?
A system of linear equations has infinite solutions when the graphs are the exact same line.
Why do some equations have infinite solutions?
If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions. If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.
Why can a linear equation have many solutions?
If two lines are coincident (i.e. the same line), then they intersect at all points along the line – that is, infinitely many points and hence infinitely many solutions. If two lines are parallel (and non-coincident) then they do not intersect and there is no solution.
Can we have infinite solution of a linear equation in one variable?
For a single Linear Equation, the values for the variables can be having infinite number of solutions possible. So x and y can have various values depending on each other’s value. Well Infinite here doesn’t mean that it is indeterminate.
How does an equation have infinite solutions?
The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.
What equations have infinite solutions?
An infinite solution has both sides equal. For example, 6x + 2y – 8 = 12x +4y – 16. If you simplify the equation using an infinite solutions formula or method, you’ll get both sides equal, hence, it is an infinite solution.
What is an equation that has an infinite number of solutions called?
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.