Answer:
L = 10.037
W = 2.291
LW = 23..........Equation 1
L = 7W - 6.......Equation 2
*Substitute the value of L to the first equation to solve for W
[tex]LW=23[/tex][tex](7W-6)W=23[/tex][tex]7W^2-6W=23[/tex][tex]7W^2-6W-23=0[/tex]
Through quadratic formula, we can get:
[tex]W=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(7)(-23)}}{2(7)}[/tex][tex]W=\frac{6\pm2\sqrt[]{170}}{14}[/tex][tex]W=\frac{3\pm\sqrt[]{170}}{7}[/tex][tex]W=2.291,\text{ }W=-1.434[/tex]
*Since we cannot have a negative value for the dimensions, we will consider 2.291.
Going back to the second equation, substitute the value of W to solve for L.
[tex]L=7W-6[/tex][tex]L=7(2.291)-6[/tex][tex]L=10.037[/tex]
The length of the garden should be 10.037 feet, and the width should be 2.291 feet.
