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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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Systems of Linear Equations

A system of equations consists of two or more equations, each of which contains at least one variable. Here are three examples:

 System 1 System 2 System 3 3x + y 4x - 2y = -5= 7 -7x + 9y 3y = 0= 8 5x - 4y y = 11= 3x + 1

Each system is called a linear system in two variables. This is because the graph of each equation is linear (that is, the graph is a straight line) and two variables are involved.

An ordered pair, (x, y), is a solution of a linear system of equations in two variables if the ordered pair makes each equation true. An ordered pair that is a solution is said to satisfy the system.

Example 1

Determine if (5, -2) is a solution of this system.

 3x - 4yx + y = 23= 3 First equationSecond equation

Solution

In each equation, replace x with 5 and y with -2. Then simplify.

 First equation Second equation Is Is Is 3x 3(5) 15 -- + 4y 4(-2) 8 23 = 23= 23 ? = 23 ? = 23 ? Yes Is Is x (5) ++ y (-2) 3 = 3= 3 ? = 3 ? Yes

Since (5, -2) satisfies each equation, it is a solution of the system.

The solution can be written as x = 5 and y = -2, or simply (5, -2).