Final answer:
To solve the system of equations given, add both equations to eliminate the y terms and find x = 5. Then, substitute x into either of the original equations to find y = 13.
Step-by-step explanation:
To solve the system of equations 3y - 4x = 19 and -3y + 8x = 1, we can use the method of addition. First, we need to align the equations vertically and simply add them, as they are setup in a way that the y terms will cancel each other out.
3y - 4x = 19
-3y + 8x = 1
Add both equations:
0y + 4x = 20
Now, we solve for x:
4x = 20
x = 5
Next, substitute this value of x into one of the original equations to find y.
We will use the first equation:
3y - 4(5) = 19
3y - 20 = 19
3y = 39
y = 13
The solution to the system of equations is x = 5 and y = 13.