Math - Systems Of Linear Equations

Front 1

Two linear equations with two or more variables are called:

Back 1

systems of linear equations or simultaneous linear equations

Front 2

A solution for a system of equations is:

Back 2

an ordered pair

Front 3

What are the methods for solving systems of linear equations?

Back 3

1) Graphical method
2)Substitution method
3) Elimination method (addition & subtraction method)

Front 4

What are the steps for solving systems of linear equations by the Graphical method?

Back 4

1) Graph each equation.
2) Locate the point of intersection of the lines.
3) The ordered pair of the point of intersection is the solution.

Front 5

What are the three types of graphs for systems of equations?

Back 5

1) Independent equations
2) Dependent equations
3) Inconsistent equations

Front 6

Describe the graph of an Independent equation:

Back 6

There is one point of intersection for the two lines; one ordered pair.

Front 7

Describe the graph of a Dependent equation:

Back 7

There is only one line for the two given equations. Every point on the line is a solution; there are an infinite number of solutions.

Front 8

Describe the graph of an Inconsistent equation:

Back 8

The graphs of the two equations will be parallel lines. There will never be an intersection; there is no solution.

Front 9

What are the steps for solving a system of linear equations using the substitution method?

Back 9

Take for example, equations A & B.
1) Isolate y in terms of x in equation B.
2) In equation A, substitute this term of x for y.
3) Simplify to isolate x.
4) Now substitute this value of x into B and solve for y.

Front 10

What are the different methods for solving a system of linear equations using the elimination method?

Back 10

1) If two of the equations have the same coefficient, then subtract the equations and substitute the answer into one of the original equations.
2) If two of the coefficients are the additive inverse of each other, then add the equations and substitute the answer into one of the original equations.
3) If one of the coefficients is a multiple of the other coefficient, multiply the smaller coefficient by a number so that it is equal or the inverse of the other and then add or subtract them. Then substitute the answer into one of the original equations.
4) If the coefficients do not have a common factor (they are prime numbers for example), then multiply each equation by the coefficient of the other and either add or subtract the equations. Then substitute the answer into one of the original equations.
5) If there is a common factor between the coefficients, then multiply both by a number so that they are both equal to their lowest common denominator and either add or subtract the equations. Then substitute the answer into one of the original equations.