Solving Systems by Substitution

Front

What is a system of equations?

Back

A set of two or more 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 the context of 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 is the first step in solving a system by substitution?

Back

Make sure at least one equation is solved for one variable.

Front

What does it mean if two lines are parallel in a system of equations?

Back

There is no solution to the system because the lines never intersect.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

If the two equations represent the same line, they have infinitely many solutions.

Front

What is the solution to the system: y = 2x - 11 and -3y = -6x - 15?

Back

No solution (parallel lines).

Front

What is the solution to the system: y = -3x + 11 and y = -6x - 13?

Back

(-8, 35).

Front

What is the solution to the system: y = -2x + 5 and y = 2x - 11?

Back

(4, -3).