Final answer:
To solve the given system of equations by elimination, we can add the two equations together to eliminate the variable 'x'. This will result in a new equation with only one variable, 'y'.
Then, we can solve for 'y' and substitute that value back into one of the original equations to solve for 'x'. The solution to the system is x = -42 and y = -13.
Step-by-step explanation:
The given system of equations is:
3y - x = 3 ...(1)
1 - 4y - x = 10 ...(2)
To solve this system of equations, we can use the method of elimination.
We can eliminate the variable 'x' by adding equations (1) and (2) together:
(3y - x) + (1 - 4y - x) = 3 + 10
Simplifying, we get:
3y - 4y = 13
-y = 13
Dividing by -1, we get:
y = -13
Now, substitute this value of 'y' back into either equation (1) or equation (2) to solve for 'x'.
Let's substitute it into equation (1):
3(-13) - x = 3
-39 - x = 3
Adding x to both sides:
-39 = x + 3
Subtracting 3 from both sides:
-42 = x
So the solution to the system of equations is:
x = -42, y = -13