Verified Answer :

luana

\(\left \{ {{4x+2y=26} \atop {4x-3y=51\ \ | *(-1)}} \right. \\\\ \left \{ {{4x+2y=26} \atop {-4x+3y=-51}} \right. \\\\+----\\addition\\\\ 5y=-25\ \ \ | divide\ by\ 5\\\\ y=-5\\\\ 4x=26-2y\ \ \ | divide\ by\ 4\\\\x=\frac{13-y}{2}=\frac{13+5}{2}=9\\\\Solution:\\x=9\ and\ y=-5\)

I shall use subtraction because I see two like
terms of the same value (4x).

Set them up as a vertical subtraction problem and subtract down.

4x+2y=26
-(4x-3y=51)
___________
5y=-25

Solve for y.

y=-5

Plug this value of y into either original equation and solve for x.

4x+2(-5)=26
4x-10=26
4x=36

x=9

Therefore, the solution is (9, -5).