Final answer:
To solve the system of linear equations by elimination, multiply the equations to make the coefficients of x the same, subtract the equations to eliminate x, divide by the coefficient of y to solve for y, and substitute y back into one of the original equations to solve for x.
Step-by-step explanation:
To solve the system of linear equations by elimination, we need to eliminate one variable by adding or subtracting the equations.
To eliminate variable x, we can multiply the first equation by 6 and the second equation by 9 to make the coefficients of x the same. This gives us:
54x + 12y = 234 and 54x + 117y = -81
Next, subtract the two equations to eliminate x: (54x + 117y) - (54x + 12y) = -81 - 234. Solve for y to get: 105y = -315. Dividing both sides by 105, we find that y = -3.
Finally, substitute y = -3 back into one of the original equations to find x: 9x + 2(-3) = 39. Simplifying, we get 9x - 6 = 39. Adding 6 to both sides, we have 9x = 45. Dividing by 9, we find that x = 5.