Final answer:
To solve the system using elimination, we first make the coefficients of y the same and then eliminate y by subtracting one equation from the other, resulting in y = -2. We then substitute y = -2 back into one of the original equations to find x = -2.
Step-by-step explanation:
To solve the system of equations using elimination, we must first make the coefficients of either x or y the same in both equations. For instance, we can multiply the first equation by 2 and the second equation by 7 to make the coefficients of y the same:
- (7x - 6y = -2) × 2 → 14x - 12y = -4
- (2x - 7y = 10) × 7 → 14x - 49y = 70
Next, we eliminate terms by subtracting the second new equation from the first new equation:
- 14x - 12y - (14x - 49y) = -4 - 70
- 14x - 12y - 14x + 49y = -74
- 37y = -74
- y = -74 / 37
- y = -2
Now, substitute y = -2 into one of the original equations to solve for x:
- 7x - 6(-2) = -2
- 7x + 12 = -2
- 7x = -14
- x = -2
The solution to the system of equations is x = -2 and y = -2. Finally, we check the answer to see if it is reasonable by plugging the values of x and y back into the original equations.