5.2 Solving Systems of Linear Equations by Substitution

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is substitution in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What does it indicate if a system of equations has no solution?

Back

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

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

The lines intersect at exactly one point.

Front

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

Back

Solve one of the equations for one variable in terms of the other.

Front

If y = 2x + 3, what is y when x = 1?

Back

y = 5.

Front

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

Back

(1, 4).

Front

What does the equation 4 = 7 signify in terms of solutions?

Back

It indicates no solution, as it is a false statement.