Solving a System of Linear Equations in Two Variables - Concept

Concept Concept (1)

A system of linear equations is two or more equations that contain the same variables. A solutions to a system of equations are the point where the lines intersect. There are four methods to solving systems of linear equations: graphing, substitution, elimination and matrices. Solving systems of equations first shows up in Algebra I, but more complex applications occur in Algebra II.

Sample Sample Problems (18)

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Solving a System of Linear Equations in Two Variables - Problem 1

Solve the system:

4x − 2y = 7
x + 2y = 3
Problem 1
How to solve a system of linear equations in two variables with substitution.
Solving a System of Linear Equations in Two Variables - Problem 2

Solve the system:

2x − 4y = 3
-5x + 10y = 7
Problem 2
How to solve a system of linear equations using elimination that yields no solution.
Solving a System of Linear Equations in Two Variables - Problem 3

Solve the system:

6x + 21y = 12
x + 7 y = 2
2
Problem 3
How to solve a system of linear equations using elimination that yields parallel lines.
Solving a System of Linear Equations in Two Variables - Problem 4
Problem 4
Strategies for when and how to use substitution to solve a 2 x 2 system of equations.
Solving a System of Linear Equations in Two Variables - Problem 5
Problem 5
Strategies for when and how to use graphing to solve a 2 x 2 system of equations.
Solving a System of Linear Equations in Two Variables - Problem 6
Problem 6
Strategies for how and when to use elimination to solve a 2 x 2 system of equations.
Solving a System of Linear Equations in Two Variables - Problem 7
Problem 7
How to use a TI graphing calculator to solve a 2 x 2 system of linear equations graphically.
Solving a System of Linear Equations in Two Variables - Problem 8
Problem 8
Overview of solving word problems using a 2 variable system of equations.
Solving a System of Linear Equations in Two Variables - Problem 9
Problem 9
How to choose a method for solving a 2 x 2 system of linear equations.
Solving a System of Linear Equations in Two Variables - Problem 10
Problem 10
Vocabulary and special cases of 2 x 2 systems including inconsistent, dependent, consistent, infinite solutions, and no solutions.
Solving a System of Linear Equations in Two Variables - Problem 11
Problem 11
Solving mixture word problems using a 2 x 2 system of equations.
Solving a System of Linear Equations in Two Variables - Problem 12
Problem 12
Solving word problems with a starting amount and fixed change using a 2 x 2 system of equations.
Solving a System of Linear Equations in Two Variables - Problem 13
Problem 13
Solving coin word problems using a 2 x 2 system of equations.
Solving a System of Linear Equations in Two Variables - Problem 14
Problem 14
Solving rate word problems, including water and air current, using a 2 x 2 system of equations.
Solving a System of Linear Equations in Two Variables - Problem 15
Problem 15
Linear programming or using a system of linear inequalities to maximize or minimize an objective function.
Solving a System of Linear Equations in Two Variables - Problem 16
Problem 16
Solving a digits word problem using a 2 x 2 system of equations.
Solving a System of Linear Equations in Two Variables - Problem 17
Problem 17
Solving a system of equations with a line and a parabola graphically and using substitution.
Solving a System of Linear Equations in Two Variables - Problem 18
Problem 18
Solving a work, or shared job word problem using a 2 x 2 system of equations.