Systems of Equations All Methods

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 the elimination method involve?

Back

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

Front

How do you solve a system of equations using substitution?

Back

To solve using substitution, isolate one variable in one equation and substitute that expression into the other equation.

Front

What is the graphical method of solving systems of equations?

Back

The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

Front

What is the first step in the elimination method?

Back

The first step is to align the equations and manipulate them (if necessary) so that adding or subtracting them will eliminate one variable.

Front

Solve using elimination: 4x + 9y = 28 and -4x - y = -28.

Back

(7, 0)

Front

Solve using elimination: 3x + 2y = 16 and 7x + y = 19.

Back

(2, 5)

Front

Which method is best for isolating a variable?

Back

The substitution method is best for isolating a variable.

Front

What is the purpose of writing a system of equations?

Back

The purpose is to model real-world situations where multiple conditions must be satisfied simultaneously.

Front

What does it mean if two equations are dependent?

Back

Dependent equations have infinitely many solutions; they represent the same line in a graph.