Systems of Equations by Substitution and Elimination

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 by substitution?

Back

Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What does it mean to solve a system of equations by elimination?

Back

Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, meaning they never intersect.

Front

How do you determine if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning they overlap completely.

Front

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

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

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

Back

The first step is to align the equations and manipulate them (if necessary) to have the coefficients of one variable be opposites.

Front

Solve the system by substitution: y = 2x + 3, 3x - y = 5.

Back

(1, 5)

Front

Solve the system by elimination: 2x + 3y = 6, 4x - 3y = 12.

Back

(3, 0)

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines represented by the equations.