Systems-Substitution Method

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

Back

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

Front

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

Back

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

Front

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

Back

A unique solution exists if the lines intersect at exactly one point.

Front

Solve the system: 2x + 3y = 6 and x - y = 1.

Back

(3, 0)

Front

What is the first step in the substitution method?

Back

Isolate one variable in one of the equations.

Front

If two equations are equivalent, what can be said about their solutions?

Back

They have the same solution set.

Front

Solve the system: y = 3x + 2 and y = -x + 4.

Back

(0.67, 3.02)

Front

What is the graphical representation of a system with no solution?

Back

Two parallel lines that never intersect.

Front

What is the graphical representation of a system with infinite solutions?

Back

Two overlapping lines that are the same.