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 if a system of equations has infinite solutions?

Back

It means that the equations represent the same line, and there are countless points (x, y) that satisfy both equations.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines that never intersect.

Front

Solve the system: 3x - 4y = -2 and y = 2x + 1.

Back

(1, 3)

Front

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

Back

(5, -4)

Front

Solve the system: x + y = 19 and y = 3x - 1.

Back

(5, 14)

Front

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

Back

(5, 4)

Front

What is the first step in the substitution method?

Back

The first step is to solve one of the equations for one variable.