What happens when a variable cancels out?

If the variables cancel out, there is no variable and you just get a numeric statement (which may or may not be true since it has been incorrectly constructed). that the equation(s) have been incorrectly derived.

How do you solve a system of equations when both variables cancel out?

If both x and y are going to cancel out, then you have either no solution or infinitely many solutions. If the constant on the right are going to cancel out (same number with opposite signs) then there are infinitely many solutions (same line).

What happens when both variables cancel out in elimination?

If both variables are eliminated and you are left with a true statement, this indicates that there are an infinite number of ordered pairs that satisfy both of the equations. In fact, the equations are the same line. Solve for x and y.

What does it mean when a simultaneous equation has no solution?

System of Linear Equations with No Solutions A system has no solutions if two equations are parallel. When two equations have the same slope but different y-axis, they are parallel. Since there are no intersection points, the system has no solutions.

When solving equations if the variables cancel out and the remaining equation is true you have?

If your variable drops out and you have a FALSE statement, that means your answer is no solution. If your variable drops out and you have a TRUE statement, that means your answer is infinite solutions, which would be the equation of the line. Step 6: Check the proposed ordered pair solution in BOTH original equations.

What is the solution if all variables cancel when solving a system and you are left with a false statement?

If both variables drop out and you have a FALSE statement, that means your answer is no solution. If both variables drop out and you have a TRUE statement, that means your answer is infinite solutions, which would be the equation of the line.

How do you solve systems of equations by elimination?

To Solve a System of Equations by Elimination

1. Write both equations in standard form.
2. Make the coefficients of one variable opposites.
3. Add the equations resulting from Step 2 to eliminate one variable.
4. Solve for the remaining variable.
5. Substitute the solution from Step 4 into one of the original equations.

How do you solve for no solution?

To create a no solution equation, we can need to create a mathematical statement that is always false. To do this, we need the variables on both sides of the equation to cancel each other out and have the remaining values to not be equal.

How do you find out if a system of equations has no solution?

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.