Final answer:
Multiply the second equation by 3 to make the coefficients of y in both equations have the same magnitude but opposite signs, allowing for elimination. Add the new equations to solve for x, then substitute back to find y.
Step-by-step explanation:
To solve the system of equations by elimination, we first want to write both equations in a way that facilitates the elimination of one of the variables. Given the equations 5x - 6y = -2 and -3x + 6 = 2y, the second equation can be rearranged to -3x - 2y = -6. In order to eliminate the variable y, we can multiply the entire second equation by 3 (not by -5 as the system is slightly mistyped in your question). This will result in the coefficients of y in both equations having the same magnitude but opposite signs.
Multiplying the second equation by 3 gives: -9x - 6y = -18.
Now, the two equations are:
- 5x - 6y = -2
- -9x - 6y = -18
We can then add these two equations together to eliminate the y variable and find the value of x. Afterward, you substitute the found value of x back into one of the original equations to solve for y, thus finding the solution of the system of equations.