Algebra - Topic 4: Systems (Substitution/Elimination)

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 set of values that satisfy all equations in the system.

Front

What does substitution mean in solving systems of equations?

Back

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

Front

What does elimination mean in solving systems of equations?

Back

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

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the same situation.

Front

What is the solution to a system of equations?

Back

The solution is the point (or points) where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

Isolate one variable in one of the equations.

Front

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

Back

Align the equations and manipulate them (if necessary) to have the same coefficients for one of the variables.

Front

If a system of equations has no solution, what does that mean?

Back

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

Front

If a system of equations has infinite solutions, what does that mean?

Back

It means the equations represent the same line, and there are countless points of intersection.

Front

Solve the system by substitution: x + 2y = 2, x = -4y + 2. What is the solution?

Back

(2, 0)