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Solving Systems of Linear Equations using Elimination

Solving Systems of Linear Equations using Elimination 1.5 - Solution

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a

A rectangle has two equally long sides, called length, and two equally short sides, called width. If we denote the length and the width and respectively we can draw the following figure.

the Rectangle with long side l and the short side w

The rectangle has a perimeter of m. By adding the four sides of the rectangle the sum must equal This we can write as an equation. The rectangle's length is m longer than its width. Therefore, if we subtract from the difference becomes This gives us the following equation. Together, they form a system of equations.

b
We can find and by solving the system using the elimination method. It is then necessary that one of the variable terms is eliminated when one equation is added to or subtracted from the other equation. In its current state, this won't happen. Therefore, we need to manipulate one or both equations. If we multiply Equation (II) by the -terms will have opposite coefficients.
Now we have the following system. If we add the equations we will eliminate the -terms. By solving the resulting equation we find To find the width of the field we can substitute for in the equation
Thus, the field has a length of m and a width of m.