Final answer:
To solve this system of equations using the elimination method, we can eliminate the variable 'x' by multiplying the first equation by 2 and subtracting it from the second equation. The resulting equations are -5x + 2y = -9 and 5x + 4y = -9. These equations can be solved using various methods.
Step-by-step explanation:
To solve these two equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations. In this case, we can eliminate the variable 'x' by multiplying the first equation by 2 and subtracting it from the second equation.
Multiplying the first equation by 2, we get: 10x = 2(y + 6). Expanding, we have: 10x = 2y + 12.
Now subtracting this equation from the second equation, we have: (5x + 2y) - (10x) = 3 - 12. Simplifying, we get: -5x + 2y = -9. This equation represents a line in the x-y plane.
The next step is to solve these two equations for the variable 'y'. Substituting 'y' in the second equation for '5x + 2y', we have: -5x + 2(5x + 2y) = -9. Expanding and simplifying, we get: 5x + 4y = -9.
Now we have two equations: -5x + 2y = -9 and 5x + 4y = -9. We can solve these equations using various methods such as substitution or graphing to find the solution to the system of equations.