Answer:
[tex]x=3[/tex]
[tex]y=\frac{17}{8}[/tex]
Step-by-step explanation:
Firstly, we have to transform what is written in words to equations.
The sum of two numbers is 41/8
If we call the unknown numbers as [tex]x[/tex] and [tex]y[/tex], we will have:
[tex]x+y=\frac{41}{8}[/tex] (1)
Their difference is 7/8
[tex]x-y=\frac{7}{8}[/tex] (2)
Now we have a system with two equations and two unknowns. Let's solve it.
Isolating [tex]x[/tex] from (1):
[tex]x=\frac{41}{8}-y[/tex] (3)
Substituting (3) in (2):
[tex]\frac{41}{8}-y-y=\frac{7}{8}[/tex] (4)
Isolating [tex]y[/tex]:
[tex]\frac{41}{8}-\frac{7}{8}=2y[/tex]
[tex]y=\frac{34}{16}=\frac{17}{8}[/tex] (5) This is the value of y
Substituting (5) in (1):
[tex]x+\frac{17}{8}=\frac{41}{8}[/tex] (6)
Finding [tex]x[/tex]:
[tex]x=\frac{41}{8}-\frac{17}{8}[/tex]
[tex]x=3[/tex] (7) This is the value of x
