Table of Contents
- 1 How do we know if two linear equations have infinitely many solutions?
- 2 Is it true that a linear equation has infinitely many solutions when both sides of the equation are equivalent?
- 3 How do you determine if a system of equations has infinite solutions?
- 4 What does it mean when an equation has infinitely many solutions?
- 5 Why can’t a linear system have 2 solutions?
- 6 Can two distinct solutions to the equation intersect?
How do we know if two linear equations have infinitely many solutions?
The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. In other words, when the two lines are the same line, then the system should have infinite solutions.
Is it true that a linear equation has infinitely many solutions when both sides of the equation are equivalent?
Equations with an infinite number of solutions If a linear equation has the same variable term and the same constant value on both sides of the equation, it has infinitely many solutions.
How do you determine if a system of equations has infinite solutions?
A system of linear equations has infinite solutions when the graphs are the exact same line.
How many solutions can a system of 2 linear equations in 2 variables have?
A linear equation in two variables, such as 2x+y=7, has an infinite number of solutions. Its graph is a line. Remember, every point on the line is a solution to the equation and every solution to the equation is a point on the line.
How do you know if a linear system has infinite solutions?
What does it mean when an equation has infinitely many solutions?
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.
Why can’t a linear system have 2 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 two distinct solutions to the equation intersect?
Two distinct solutions of x′(t)=f(x(t)) cannot intersect at any point.
How do you find 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.