Warm Up Systems of Equations Substitution Method

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 the substitution method involve?

Back

Replacing one variable in a system of equations with an expression derived from another equation.

Front

How do you determine if a system of equations has one solution?

Back

If 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

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

The equations represent the same line, meaning every point on the line is a solution.

Front

How can you represent the cost of apples and bananas in equations?

Back

Using variables, for example: let x = cost of apples and y = cost of bananas.

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.

Front

If you have the equations 4x + 6y = 13 and 3x + 7y = 13.5, what do you do next?

Back

Use substitution to express one variable in terms of the other and solve.

Front

What is the solution to the system of equations 2x + 3y = 6 and x - y = 1?

Back

(3, 0) is the solution.

Front

What does it mean for two equations to be dependent?

Back

They represent the same line and have infinitely many solutions.