Systems: Elimination and Substitution

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 when a system of equations has no solution?

Back

A system has no solution when the lines representing the equations are parallel and never intersect.

Front

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

Back

A system has infinite solutions when the equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

A system has one solution when the lines intersect at exactly one point, meaning they have different slopes.

Front

Solve the system: 2x + 3y = -2 and 3x - 2y = 23.

Back

(5, -4)

Front

Solve the system: 3x + y = 19 and 2x - y = 6.

Back

(5, 4)

Front

Which method is best for solving the system: 3x - 4y = -2 and y = 2x + 1?

Back

Substitution.

Front

What is the solution to the system: 2x + 3y = 1 and 4x - y = 3?

Back

(1, -1)