Final answer:
The solution to the system of equations 6x+2y=6 and 7x+3y=5 is achieved by the elimination method, resulting in x=2 and y=-3.
Therefore, the correct answer is option c) (2, -3).
Step-by-step explanation:
To find the solution to the system of equations 6x+2y=6 and 7x+3y=5, we can use either the substitution or the elimination method. Let's use the elimination method to solve for x and y.
First, we make the coefficients of y the same in both equations. We can multiply the first equation by 3 and the second equation by 2.
This gives us 18x + 6y = 18 and 14x + 6y = 10.
Subtracting the second equation from the first, we get 18x - 14x = 8 which simplifies to 4x = 8.
Dividing both sides by 4, we find x to be 2.
To find y, we substitute x back into one of the original equations, for example into the first one 6x+2y=6:
Substituting x = 2 into the equation, we have 6(2)+2y=6 which simplifies to 12+2y=6.
Subtracting 12 from both sides gives 2y = -6, and dividing by 2 gives y to be -3.
Thus, the solution is (2, -3), which corresponds to option c.