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

If a system of equations has infinite solutions, what does that imply?

Back

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

Front

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

Back

The equations represent parallel lines that never intersect.

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into both equations to see if they hold true.

Front

Solve the system: x = -3y - 8 and x - 2y = -3.

Back

(-5, -1)

Front

Solve the system: y = -1x - 5 and 4x - 8y = 4.

Back

(-3, -2)

Front

Solve the system: 6x + y = -1 and y = -3x - 4.

Back

(1, -7)