Substitution/Elimination 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 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 variable.

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 infinite solutions?

Back

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

Front

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

Back

If the lines intersect at exactly one point, the system has one unique solution.

Front

Solve by elimination: 2x + 3y = 6 and 4x + 6y = 12. What is the solution?

Back

Infinite solutions.

Front

Solve by substitution: y = 2x + 3 and x + y = 7. What is the solution?

Back

(2, 3).

Front

What is the first step in the elimination method?

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

If you have the equations 3x + 2y = 12 and 3x + 2y = 6, what can you conclude?

Back

No solution, as the lines are parallel.

Front

What is a key advantage of the substitution method?

Back

It can be easier to use when one equation is already solved for one variable.