Question

1. Solve the system: 2x + y = 5

x – y = 13

2. Bobby is three years older than twice Arianna’s age. If the total of their ages is 9, how old is Bobby, and how old is Arianna?

3. Solve the system: y = x2 + 5

6x – y = 3

Answer 1

1. We have 2x + y = 5…(1) and x – y = 13…(2).

On adding the 2 equations, we get 2x+y +x-y = 5+13 or, 3x = 18 so that x = 18/3 = 6. Then, on substituting x = 6 in the 2^nd equation, we get 6-y = 13 or, y = 6-13 = -7. Thus, x = 6 and y = -7.

2. Bobby is three years older than twice Arianna’s age. Let Ariana’s age be x years. Then, Bobby’s age is 2x+3 years. Since the total of their ages is 9, hence x+2x+3 = 9 or, 3x= 9-3 = 6 so that x = 6/3 = 2. Thus, Arianna is 2 years old and Bobby is 2*2+3 = 7 years old.

3. We have y = x² + 5…(1) and 6x – y = 3 or, y = 6x-3…(2).On substituting y = 6x-3 in the 1^st equation, we get 6x-3 = x²+ 5 or, x²-6x+8 = 0 or, x²-4x-2x+ 8 = 0 or, x(x-4)-4(x-4) = 0 or, (x-2)(x-4) = 0. Hence, either x = 2 or, x = 4.