What does it mean when a linear equation in one variable has infinitely many solutions?
Infinitely many solutions: When both sides are the same For example, some have no solutions, and others may have infinitely many. Having infinitely many solutions means that you couldn’t possibly list all the solutions for an equation, because there are infinite.
How can you tell when an equation in one variable has infinitely many solutions or no solution?
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.
Would it be possible to have a system of equations with infinitely many solutions?
An equation can have infinitely many solutions when it should satisfy some conditions. 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.
How many solutions can a linear equation with one variable have?
one solution
A linear equation in one variable cannot have more than one solution.
Which is a linear equation in one variable?
Linear Equation in One Variable. The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.
How can you tell if an equation has 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.
How do you tell if a linear system has one solution no solution or infinite solutions?
A linear system has many (infinite) solutions when the two lines are the same (such as y=x+3 and 2y=2x+6 ). And a linear system has no solution when the lines never intersect (in other words, they’re parallel; their slopes are equal).
How do you know if a linear equation has one solution?
How can a linear equation have infinite solutions?
A system of linear equations has infinite solutions when the graphs are the exact same line.
Which system type is a linear system with infinitely many solutions?
dependent system
A dependent system has infinitely many solutions. The lines are coincident. They are the same line, so every coordinate pair on the line is a solution to both equations.
Are linear equation in one variable has?
The linear equation has the highest exponent of variables as 1 and has only one variable. Therefore, the Linear equation in one variable has only one variable with power 1 . Thus, option C is the correct answer. .
How do you know if a linear equation is one variable?
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2.
How do you know if a linear equation has infinite solutions?
From the above examples we can say that, the linear equation will have infinite solutions if it is satisfied by any value of the variable or every value of the variable makes the given equation a true statement. Solve the following linear equations & identify whether the given linear equations have one , zero or infinite solutions.
Can there be a linear equation with only one variable?
Yes, it has only 1 solution. You mentioned of a “Linear Equation” with one variable, so it can be nothing other than the form; So it has only 1 solution. And always remember, linear eqauations are; In a one variable linear equation the other variables become constant , but however there must be atleast one variable in the equation unlike; etc..
How do you know if an equation has only one solution?
Hence, the given linear equation has only one solution i.e. x = 80. From the above examples, we see that the variable x does not disappear after solving & we say that the linear equation will have one solution if it is satisfied by exactly one value of the variable. Example 1: Consider the equation 7x – 35 = 5x + 2x – 27.
When does a linear equation have zero or no solution?
From the above examples, we can see that the variable x disappears / gets eliminated & hence we say that the linear equation will have Zero or no solution if it can’t be satisfied by any value of the variable or there does not exist any value of the variable which makes the given equation a true statement.