Suzette ran and biked for a total of 34 mi in 3.5 h. her average running speed was 6 mph and her average biking speed was 12.5 mph.
let x = total hours suzette ran.
let y = total hours suzette biked.
use substitution to solve for x and y. show your work. check your solution.
(a) how many hours did suzette run?
(b) how many hours did she bike?
in advance : )

First we need to write system of 2 equations with 2 variables:
x*6 + y*12.5 = 34
x+y = 3.5

for substitution we express one of variables in one of equations and put it in other equation.
x = 3.5-y

(3.5 - y)*6 + 12.5*y = 34
21 - 6y + 12.5y = 34
6.5y = 13
y = 2
x = 3.5 - y = 3.5 - 2 = 1.5

she ran for 1.5 hours and biked for 2 hours.
check:
1.5*6 + 2*12.5 = 9 + 25 = 34 = 34