Final answer:
The question involves solving linear equations, but the provided method refers to solving quadratic equations using the quadratic formula. A correct approach to linear equations involves isolating the variable 'x' through algebraic manipulation and applying basic arithmetic rules for addition and subtraction.
Step-by-step explanation:
The question appears to be related to solving linear equations and testing different option pairs as potential solutions to a given set of linear equations. However, the presented solution method seems a bit out of context as it discusses the process of solving quadratic equations using the quadratic formula, where coefficients are denoted by 'a', 'b', and 'c'. This method includes calculating the determinant (√(b² - 4ac)) and finding two possible solutions by adding or subtracting the square root of the determinant from the negative 'b' term, and then dividing by 2a. Nonetheless, this approach does not apply to the original two given linear equations, which can be solved through simpler algebraic manipulation.
Returning to the linear equations, 3x + 4 = 10 and 61 - 2 = 40 (which seems to be a typo since it simplifies to 59 = 40, an incorrect equality), we would proceed to solve the correctly stated equation by isolating 'x' through basic algebraic operations. An example would be: subtracting 4 from both sides of the equation 3x + 4 = 10, yielding 3x = 6, and then dividing by 3 to find x = 2.
Then, basic arithmetic rules dictate how addition and subtraction operations should proceed depending on the signs of the numbers involved. For instance, when subtracting a negative from a positive number, like 2 - (-6), you would actually add the absolute values to get 2 + 6 = 8. These rules are essential when working with both simple and complex equations throughout mathematics.