Solving systems of equations 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 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 of equations by substitution?

Back

Isolate one variable in one of the equations.

Front

If two lines are parallel, what does that indicate about their system of equations?

Back

The system has no solution.

Front

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

Back

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

Front

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

Back

Substitute the values back into the original equations to see if they hold true.

Front

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

Back

No solution (the lines are parallel).

Front

What is the solution to the system of equations: x + 2y = 2 and x = -4y + 2?

Back

(2, 0).

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.