Final answer:
By solving the system of linear equations x + y = 63 and x - y = 7, we find that the two numbers are 35 and 28.
Step-by-step explanation:
The problem given is a system of linear equations that can help us find two unknown numbers. The equations given are: 1) the sum of the two numbers is 63, and 2) their difference is 7. To solve this, we can set up the equations as x + y = 63 and x - y = 7. By solving these simultaneously, we can find the values of x and y.
To solve the system using substitution, let's express y in terms of x from the first equation: y = 63 - x. Now, plug this expression into the second equation: x - (63 - x) = 7, which simplifies to 2x - 63 = 7. Solving this equation for x gives us x = 35. To find y, we substitute x back into the equation y = 63 - x, getting y = 63 - 35, which gives us y = 28.
The two numbers we are looking for, therefore, are 35 and 28.