Systems Elimination (Easy)

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution to a system of equations if it satisfies all equations in the system when substituted for the variables.

Front

How do you check if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into each equation. If both equations are true, the point is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection of the lines represented by each equation on a coordinate plane.

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What does it mean if two lines in a system of equations are parallel?

Back

If two lines are parallel, they have no points of intersection, meaning there is no solution to the system.

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What does it mean if two lines in a system of equations coincide?

Back

If two lines coincide, they are the same line, meaning there are infinitely many solutions to the system.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, which can be either a single point or infinitely many points.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, typically represented by parallel lines.