Let
y ----> amount in the saving account
x ----> number of weeks
The linear equation is of the form
y=mx+b
where
m is the slope or unit rate
b is the y-intercept or initial value
so
Lyle
we have
m=$20 per week
b=$100
y=20x+100 -----> Lyle's linear equation
Shaun
we have
m=$10 per week
b=$500
y=10x+500 ------> Shaun's linear equation
Equate both equations
20x+100=10x+500
20x-10x=500-100
10x=400
x=40
In 40 weeks they have the same amount in the savings account
therefore
The answer is 40 weeks
