Systems of Equations

Question

1. The sum of two numbers is 53. If their difference is 25, find both numbers.
Variables: 53,23	Solve:
System:	Solution:

Answer 1

Systems of Equations: The sum of two numbers is 53. If their difference is 25, find both numbers.

Detailed Solution:

Let the two numbers be: x and y

Sum of two numbers is 53: x + y = 53 ==> Equation 1

Difference of two numbers is 25: x – y = 25 ==> Equation 2

Equation 1 + Equation 2=>(x + y = 53) + (x – y = 25)=>(x + x + y – y = 53 + 25)=>(2x = 78) => x = 39

x + y = 53 => y = 53 – x => y = 53 – 39 => y = 14

The two numbers are: x = 39 and y = 14

Check: (x + y = 53) & (x – y = 25)=>(39 + 14 = 53) & (39 – 14 = 25)=>(53 = 53) & (25 = 25)

Answer 2

x + y = 53

x - y = 23

2x = 76

Can you solve for x and answer?