Solving Systems by Substitution

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where one variable is expressed in terms of the other variable, allowing us to solve equations with one variable at a time.

Front

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

Back

It means that the equations represent the same line, resulting in coinciding lines (overlapping) on a graph.

Front

How do you perform substitution in a system of equations?

Back

To perform substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

What is the first step in solving a system of equations by substitution?

Back

Identify one equation and solve it for one variable in terms of the other variable.

Front

What does the graph of parallel lines indicate about a system of equations?

Back

Parallel lines indicate that the system has no solution, as the lines never intersect.

Front

What is the purpose of substitution in solving equations?

Back

It simplifies the problem by reducing the number of variables, allowing for easier solving.

Front

What is the correct substitution for the system: 3x + (4x + 1) = 1?

Back

3x + (4x + 1) = 1.

Front

What is the correct substitution for the system: x + 2y = -4y + 2?

Back

(-4y + 2) + 2y = 2.

Front

What is the correct substitution for the system: 3x - 3y = -5x - 17?

Back

3x - 3(-5x - 17) = 3.

Front

What does it mean if two equations are equivalent?

Back

It means they represent the same line and have the same solutions.