Systems of Equations (Substitution)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

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

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

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

Back

Substitute the point's coordinates into both equations. If both equations are true, the point is a solution.

Front

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

Back

It means there is no solution to the system, as the lines never intersect.

Front

What is the graphical representation of a system of equations?

Back

It is the intersection point(s) of the lines represented by the equations.

Front

How can you tell if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

What is the solution to the system: 2x + 3y = 6 and y = 2x - 4?

Back

(2, 0) is the solution.

Front

What does it mean for a system of equations to have a unique solution?

Back

It means the lines intersect at exactly one point.

Front

What is the first step in solving a system of equations using substitution?

Back

Solve one of the equations for one variable in terms of the other.