8x + y = 21 (1)
22x - 2y = 34 (2)
To solve this system of the equation we will use the elimination method
Since y has opposite signs, then we will make their coefficients equal and add the equations
Multiply equation (1) by 2 to eleminate y
2(8x) + 2(y) = 2(21)
16x + 2y = 42 (3)
Now add equations (2) and (3)
(22x + 16x) + (2y - 2y) = (34 + 42)
38x + 0 = 76
38x = 76
Divide both sides by 38 to find x
x = 2
Now let us find y
Substitute the value of x in equation (1) or (2) to find y
I will substitute it in (1)
8(2) + y = 21
16 + y = 21
Subtract 16 from both sides to find y
16 - 16 + y = 21 - 16
y = 5
The solution of the system of equation is (2, 5)