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Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have an infinite number of solutions?

Back

It means that the equations represent the same line, and any point on that line is a solution.

Front

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

Back

Substitute the point's coordinates into each equation. If all equations are satisfied, the point is a solution.

Front

What is the graphical representation of a system of equations?

Back

The solutions are represented by the points where the graphs of the equations intersect.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

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

Back

It means the system has no solution, as the lines never intersect.

Front

What is the solution to the system of equations: x + 4y = -3 and x + 7y = -12?

Back

(9, -3)

Front

What is the solution to the system of equations: 3x + y = -14 and -2x - y = 9?

Back

(-5, 1)

Front

What is the solution to the system of equations: -4x - 4y = 0 and 4x + 4y = 0?

Back

Infinite number of solutions.