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 the context of solving equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to get the variable alone on one side of the equation.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other.

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, so every point on the line is a solution.

Front

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

Back

(1, 3).

Front

Solve the system: 2x + 3y = 6 and y = 2 - x. What is the solution?

Back

(0, 2).