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 another 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 y = 2x + 3, what is y when x = 4?

Back

y = 2(4) + 3 = 11.

Front

What does it mean 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

Solve the system: y = 3x + 1 and 2x - y = 4. What is the solution?

Back

(1, 4)

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines represent the solutions to the system.

Front

How can you check your solution to a system of equations?

Back

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