Math

To find a + b - c, we can use the given equations. 1. a + b + c = 12 2. a - b - c = 4 We can add these two equations: (a + b + c) + (a - b - c) = 12 + 4 2a = 16 a = 8 Now we can substitute a back into one of the original equations to find b and c. Using the first equation: 8 + b + c = 12 b + c = 4 (Equation 3) Next, we can substitute a into the second equation: 8 - b - c = 4 -b - c = -4 b + c = 4 (Consistent with Equation 3) Now we want to find a + b - c: a + b - c = 8 + b - c. From Equation 3 (b + c = 4): c = 4 - b. Substituting this value of c into a + b - c: 8 + b - (4 - b) = 8 + b - 4 + b = 8 + 2b - 4 = 4 + 2b. Since b + c = 4 is consistent but we don't have enough information to determine b or c individually, we can't give a precise numerical answer. Thus, we conclude: a + b - c = 4 + 2b.