The problem asks you to solve the system of equations using the elimination method. The given equations are:

1. $3x = 5y - 12$
2. $6x - 3y = 11$

Step 1: Rearrange equations

Let's rewrite both equations into standard form ($Ax + By = C$).

1. $3x = 5y - 12$ becomes: $3x - 5y = -12$

2. $6x - 3y = 11$ is already in standard form.

So the system is: $3x - 5y = -12$ $6x - 3y = 11$

Step 2: Elimination

To use the elimination method, we aim to cancel out one variable. Let's eliminate $x$ by aligning the coefficients of $x$. Multiply the first equation by 2 so that the coefficient of $x$ matches the second equation:

1. $2(3x - 5y = -12)$ becomes: $6x - 10y = -24$

The system now is: $6x - 10y = -24$ $6x - 3y = 11$

Step 3: Subtract equations

Subtract the second equation from the first to eliminate $x$:

$(6x - 10y) - (6x - 3y) = -24 - 11$ $6x - 10y - 6x + 3y = -35$ $-7y = -35$

Solve for $y$: $y = 5$

Step 4: Substitute $y = 5$ into one of the original equations

Substitute $y = 5$ into the first equation $3x - 5y = -12$:

$3x - 5(5) = -12$ $3x - 25 = -12$ $3x = 13$ $x = \frac{13}{3}$

Final Answer:

The solution is: $\boxed{\left(\frac{13}{3}, 5\right)}$

Let me know if you'd like additional details or help! 😊

5 Related Questions:

1. How do you verify the solution to a system of equations?
2. Can elimination always be used for solving a system of linear equations?
3. What happens if the system of equations has no solution?
4. How does elimination differ from substitution?
5. What are the graphical interpretations of systems of equations?

Tip:

When solving systems of equations, always simplify terms and double-check for arithmetic errors to avoid mistakes!