Answer:
The solution to this system of equations is:
Step-by-step explanation:
We are given that Jill has 47 bugs and counts a total 320 legs.
We can concur that by adding the total number of butterflies and the total number of tarantulas, we will get 47 bugs.
[tex]\text{tarantulas + butterflies} = 47[/tex]
We are also told that T is tarantulas and B is butterflies.
[tex]T + B = 47[/tex]
Then, we also know that butterflies have 6 legs and tarantulas have 8 legs. So, for every tarantula, we get a multiple of 8 and for butterflies, we get a multiple of 6. This gives us a new equation:
[tex]6B + 8T = 320[/tex]
Now, we can set up a system of equation.
[tex]\displaystyle \left \{ {{B + T = 47} \atop {6B + 8T = 320}} \right.[/tex]
Using the first equation, we can solve for B.
[tex]\displaystyle B + T = 47\\\\B + T - T = 47 - T\\\\B = 47 - T[/tex]
Then, we can substitute this value of B into the second equation and solve for T.
[tex]\displaystyle 6(47-T)+8T=320\\\\282 - 6T + 8T = 320\\\\282 + 2T = 320\\\\2T + 282 = 320\\\\2T + 282 - 282 = 320 -282\\\\2T = 38\\\\\frac{2T}{2}=\frac{38}{2}\\\\T = 19[/tex]
Finally, we can substitute this value of T into the first equation to solve for B.
[tex]B + 19 = 47\\\\B + 19 - 19 = 47 - 19\\\\B = 28[/tex]
Therefore, the solution to this system of equations is:
