Question

4p+2q=62

8p−q=59

Multiply 4p+2q=62 by 2, then subtract 8p−q=59 from the result.

Multiply 8p−q=59 by 2, then add the result to 4p+2q=62.

Do both strategies work for solving the system? If so why?

Answer 1

To solve the system of equations, we can multiply the equations by 2 and subtract. This strategy works for solving the system and gives the values of p and q in the system.

Step-by-step explanation:

To solve the system of equations 4p+2q=62 and 8p−q=59 using the given strategies, we can follow these steps:

1. Multiply 4p+2q=62 by 2: 2(4p+2q) = 2(62) = 8p+4q=124
2. Multiply 8p−q=59 by 2: 2(8p−q) = 2(59) = 16p−2q=118
3. Now, subtract 8p−q=59 from 8p+4q=124: (8p+4q) - (8p-2q) = 124 - 59 = 65 + 6q = 65

By simplifying this equation, we find that 6q = 0, which implies q = 0.

With the value of q, we can substitute it into one of the original equations, such as 4p+2q=62. Plugging in q=0, we find that 4p+2(0) = 62, which simplifies to 4p=62. Solving for p, we get p = 15.5.

Therefore, the solutions to the system of equations are p = 15.5 and q = 0.