# Solving Systems of Equation Worksheets

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## Systems of Equations Worksheets

 Systems of equations can be solved using elimination, substitution and matrix method. Worksheets are provided for systems of equations with two and three variables. Equations with two variables represent straight lines whereas three variables represent planes. This page focuses on solving equations and not to explain the behavior based on solutions.

### Solving Equations with Two Variables

System of equations with two variables represent two staight lines. Solving equations help to find the point of intersection of lines. If the lines are parallel, then there are no point of intersection and we have no solution. If the lines lie one over the another, then there are infinitely many solutions.Otherwise, we have point of intersection and unique solution. Problems provided in Elimination method can also be solved using substitution method.

### Elimination Method:

Elimination is the standard method to solve any system of equations. By making coefficients of like variable same, we can eliminate those variables that helps to find out value of another variable.

 Elimination method-Easy Elimination method-Hard

### Substitution Method:

Write any one of the equation in terms of x or y. Then replace another equation with these variable to bring all the terms with same variable and constant. After solving, find another variable.

 Substitution method-Easy Substitution method-Hard

### Reciprocal Equations Two Variables:

Set 1/x =a and 1/y = b. Now the equations become linear and ready to solve using either elimination or substitution method.

 Inverse method-Easy Inverse method-Hard

### Any Method:

Here is some exclusive worksheets in solving equations. Use any of the method as you are instructed in school or college.

 Solve by any method-Easy Solve by any method-Hard

### Solving Equations with Three Variables

Equations in three variables represent planes. There are three types of solutions unique, infinite and no solution. Elimination method is not as easy as in two variables. No special worksheets for elimination method is provided. But you can use the same worksheets for elimination method provided in "substitution" or "any method" column.

### Substitution Method:

Substitution method of solving equations with three varibles are usually harder than in two variables.

 Substitution method-Easy Substitution method-Hard

### Reciprocal Equations Three Variables:

Instuctions are almost same as we provided in reciprocal equations with two variables.

 Inverse method-Easy Inverse method-Hard

### Any method:

Apply any of the suitable method you are comfortable with.

 Any method-Easy Any method-Hard
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