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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Elimination Using Multiplication

## Multiplying Both Equations to Simplify the System

For some systems of equations, one equation must be multiplied by a fraction in order to make elimination by addition or subtraction possible. Since multiplication of integers is easier, both equations are multiplied by nonzero numbers so that the coefficients of a variable in the equations become equal (or opposite).

Example 1

Solve the system of equations.

2x + 9y = 7

3x + 7y = 4

Solution

One approach is to multiply the first equation by , and then subtract the resulting equation from the second one. This method works, but involves fractional arithmetic. Another approach is to multiply the first equation by 3 and the second by 2, to get an equivalent system of equations.

 3(2x + 9y = 7 ) 6x + 27y = 21 2(3x + 7y = 4 ) 6x + 14y = 8 6x + 27y = 21 ( - ) 6x + 14y = 8 Subtract the equations. 0 + 13y = 13 13y = 13 y = 1 Divide each side by 13.

Now substitute 1 for y in the second equation.

 6x + 14y = 8 6x + 14(1) = 8 Replace y with 1. 6x = -6 x = -1

The solution is ( -1, 1).

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