To solve the system of linear equations by elimination, we need to eliminate one of the variables by multiplying one or both equations by a constant so that the coefficients of one of the variables are equal in both equations. Then, we can subtract one equation from the other to eliminate that variable and solve for the remaining variable.
In this case, we can eliminate y by multiplying the first equation by -7 and the second equation by 6, so that the coefficients of y are equal in both equations:
-28x - 42y = -336
18x + 42y = 306
Adding these two equations together, we get:
-10x = -30
Dividing both sides by -10, we get:
x = 3
Now that we have solved for x, we can substitute this value into one of the original equations to solve for y. Using the first equation, we get:
4x + 6y = 48
4(3) + 6y = 48
12 + 6y = 48
Subtracting 12 from both sides, we get:
6y = 36
Dividing both sides by 6, we get:
y = 6
Therefore, the solution to the system of linear equations is x = 3 and y = 6.