### 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 Problems (18)

Need help with "Solving a System of Linear Equations in Two Variables" problems? Watch expert teachers solve similar problems to develop your skills.

Solve the system:

4x − 2y = 7
x + 2y = 3
###### Problem 1
How to solve a system of linear equations in two variables with substitution.

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.

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