System of Equations

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.

Front

What does it mean if a system of equations has one solution?

Back

It means that the lines represented by the equations intersect at exactly one point.

Front

What does it mean if a system of equations has no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

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

Front

How do you represent a system of equations graphically?

Back

You graph each equation on the same coordinate plane. The point(s) where they intersect represent the solution(s).

Front

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 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 the first step in solving a system of equations by substitution?

Back

Choose one equation and solve for one variable in terms of the other variable.

Front

What is the first step in solving a system of equations by elimination?

Back

Align the equations and manipulate them (if necessary) so that adding or subtracting them will eliminate one variable.

Front

If the equations are 2x + 3y = 6 and 4x + 6y = 12, what can you say about the system?

Back

The system has infinitely many solutions because the second equation is a multiple of the first.