What is the value of y?

$\large \begin{cases} x + y & = 5 ~~~~.....(1) \\ 3x - 4y & = 8 ~~~~.....(2) \\ \end{cases}$

Now multiplying the first equation by $4$ and doing $(1) + (2)$ .

$\begin{aligned} (4x + 4y) + (3x - 4y) & = (5 \times 4) + 8 \\ 4x + 3x & = 20 + 8 \\ 7x & = 28 \\ x & = 4. \\ \end{aligned}$

Now substituting $x = 4$ in $(1).$

$4 + y = 5 \implies y = \boxed 1.$

A warm-up solution :-

x = 5 - y , to be substitute into 3x - 4y = 8,

3(5-y) - 4y = 8 ,

15 - 3y -4y = 8

-7y = 8 -15

-7y = -7

y = 1

As simple as a,b,c :)

there are some different ways to get a sum of 5

1 + 4 2 + 3 3 + 2 4 + 1

i just used these to trial and error with x and y

great problem btw :)