### Concept (1)

A system of equations is two or more equations that contain the same variables. Solving systems of equations by elimination is one method to find the point that is a solution to both (or all) original equations. Besides solving systems of equations by elimination, other methods of finding the solution to systems of equations include graphing, substitution and matrices.

### Sample Problems (7)

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Solve using elimination. Check your solution.

y − x = 5
-5y + x = -9
###### Problem 1
How to solve a system of equations using elimination when one variable's coefficients are already additive inverses.

Solve using elimination. Check your solution.

-2x + 7y = 11
3y − 2x = 19
###### Problem 2
How to solve a system of equations using elimination when neither variable's coefficients are already additive inverses and there is a fractional answer.

Solve using elimination. Check your solution.

4x − 3y = -13
5x + 2y = 1
###### Problem 3
How to solve a system of equations using elimination when neither variable's coefficients are already additive inverses.
###### Problem 4
Solving a system of equations by elimination or linear combination when the coefficients are already additive inverses
###### Problem 5
Solving a system of equations by elimination, or linear combination, when both equations need to be multiplied by a constant
###### Problem 6
Technique for getting rid of fractions in a system of equations by multiplying an equation by the least common denominator
###### Problem 7
Solving a system of equations by elimination or linear combination by multiplying one equation by a constant