Systems Elimination (Easy)

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all equations in the system true.

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

Back

To determine if a point is a solution, substitute the x and y values of the point into each equation. If both equations are satisfied, the point is a solution.

Front

What does it mean if a point is not a solution to a system of equations?

Back

If a point is not a solution, it means that substituting the point's coordinates into at least one of the equations does not yield a true statement.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection point(s) of the lines represented by the equations on a coordinate plane.

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 variable.

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What is the substitution method in solving systems of equations?

Back

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

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution (they intersect at one or more points).

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What does it mean for two equations to be inconsistent?

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Two equations are inconsistent if they have no solutions (they are parallel lines and do not intersect).

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What is a dependent system of equations?

Back

A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.

Front

What is the importance of checking solutions in a system of equations?

Back

Checking solutions ensures that the proposed solution satisfies all equations in the system, confirming its validity.