Solve for y by using elimination
-4x + 8y = 10
7x + 9y = 19

Ok you said elimination, I included substitution and elimination, always take the easiest one, I took (Y) (8y) because it was positive, on the other equation, you can do the same, by working with the (X) (7x) because the quantity is smaller!
10= 4x-8y=
We take the (Y)=
-8 + 10y -4x=
10(-8) + 10y -4x=
2+ 10y-4=
2 - 4 + 10y
= 2+ 10y
Y= 10 -2
Y=8

-4x + 8y = 10 ⇒ -28x + 56y = 70
 7x + 9y = 19 ⇒ -28x  - 36y = -76
                                      92y = 146
                                       92      92
                                          y = 1²⁷/₄₆
                       7x + 9(1²⁷/₄₆) = 10
                         7x + 14¹³/₄₆ = 10
                               - 14¹³/₄₆  - 14¹³/₄₆
                                       7x = -4¹³/₄₆
                                        7         7
                                        x = ⁻¹⁹⁷/₂₂
                                (x, y) = (⁻¹⁹⁷/₃₂₂, 1²⁷/₄₆)