More Practice: Solving Systems 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 if two lines are parallel in a system of equations?

Back

They have no solutions because they never intersect.

Front

What is the substitution method 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

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 solution.

Front

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

Back

The two equations represent the same line, meaning every point on the line is a solution.

Front

What is the first step in solving the system using substitution?

Back

Isolate one variable in one of the equations.

Front

Given the equations y = 2x - 1 and 4x + y = 17, what is the solution?

Back

(3, 5)

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What does it mean if two lines in a system are the same?

Back

They have infinitely many solutions because they overlap completely.

Front

How can you tell if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating no solution.