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Solving Quadratic Equations by Completing the Square
Graphing Logarithmic Functions
Division Property of Exponents
Adding and Subtracting Rational Expressions With Like Denominators
Rationalizing the Denominator
Multiplying Special Polynomials
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Solving Linear Systems of Equations by Elimination
Solving Systems of Equation by Substitution and Elimination
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Solving Linear Systems of Equations by Graphing
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Solving Proportions
Parallel and Perpendicular Lines
Simplifying Square Roots
Simplifying Fractions
Adding and Subtracting Fractions
Adding and Subtracting Fractions
Solving Linear Equations
Inequalities in one Variable
Recognizing Polynomial Equations from their Graphs
Scientific Notation
Factoring a Sum or Difference of Two Cubes
Solving Nonlinear Equations by Substitution
Solving Systems of Linear Inequalities
Arithmetics with Decimals
Finding the Equation of an Inverse Function
Plotting Points in the Coordinate Plane
The Product of the Roots of a Quadratic
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Solving Quadratic Equations by Completing the Square
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Solving Linear Systems of Equations by Elimination

Use elimination to find the solution of this system.

Solution

To make the equations easier to work with:

• Clear the fractions in the first equation by multiplying both sides by 6, the LCD of the fractions.
• Clear the decimals from the second equation by multiplying both sides by 10.  10(0.3x + 0.2y = -1) 3x + 2y = -10
To make the x-coefficients opposites, multiply the transformed second equation by -1.

Add the equations.

Both variables are eliminated. The result is the false statement 0 = 31.

When the result is a false statement, the graphs of the equations never intersect. The graph confirms that the lines are parallel and have no points in common.

This system has no solution because the lines never intersect.

The system is inconsistent. (It has no solution.)

The equations of the system are independent. (Their graphs are not identical.)

Note — Solving a Linear System: Special Cases

When using either substitution or elimination, if both variables are eliminated there are two possible outcomes:

• If the resulting equation is an identity, such as 5 = 5, then the lines coincide.

The system has infinitely many solutions.

The solutions may be stated as the set of all points on the line.

• If the resulting equation is a false statement, such as 0 = 4, then the lines are parallel and never intersect.

The system has no solution.

The system is inconsistent and the equations are independent.

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