Systems of Equations - Recap

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is elimination in solving systems of equations?

Back

Elimination is a method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What does it mean for two equations to be independent?

Back

Two equations are independent if they have exactly one solution, meaning their graphs intersect at one point.

Front

What does it mean for two equations to be dependent?

Back

Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.

Front

What does it mean for two equations to be inconsistent?

Back

Two equations are inconsistent if they have no solutions, meaning their graphs are parallel and never intersect.

Front

How do you graph a system of equations?

Back

To graph a system of equations, plot each equation on the same coordinate plane and identify the point(s) where they intersect.

Front

What is the first step in solving the system: y = 2x + 3 and x + y = 5?

Back

Substitute 2x + 3 for y in the second equation: x + (2x + 3) = 5.

Front

What is the next step after simplifying: 5x - 8x + 16 = 7?

Back

Subtract 16 from each side to isolate the variable: -3x = 7 - 16.