Question

The sum of two numbers is 65. The difference of the two numbers is 27. Write and solve a system of linear equations to find the two numbers. Let x represent the greater number,and let y represent the lesser number.

Answer 1

x + y = 65 The sum of two numbers (x and y) is 65
x - y = 27 The difference of the two numbers is 27

This can easily be solved with elimination.

2x = 92
x = 46

Then we solve for y replacing the x value for x.
46 + y = 65
y = 19

The solution is (46, 19).

If you want substitution:

x + y = 65
x - y = 27

y = 65 - x
x - y = 27

x - (65 - x) = 27
x - 65 + x = 27
2x - 65 = 27
2x = 92
x = 46

Then solve for y using either equation.
46 - y = 27
- y = - 19
y = 19

We get the same solution (46, 19). You can check this by plugging in the x and y values into one or both equations.

Answer 2

The numbers whose sum is 65 and the difference is 27 are 46 and 19 and this will be determined by forming the linear equation in two variables.

Given :

• The sum of the two numbers is 65.
• The difference between the two numbers is 27.

Let 'x' represent the greater number and let 'y' represent the lesser number.

The sum of the two numbers is given by:

$x + y = 65$   --- (1)

The difference between the two numbers is given by:

$x - y = 27$

$x = 27+y$    ----- (2)

Now, put the value of 'x' in equation (1).

$27+y+y = 65$

27 + 2y = 65

2y = 38

y = 19

Now, put the value of 'y' in equation(2).

x = 27 + 19

x = 46

Therefore, the numbers are 46 and 19.

For more information, refer to the link given below:

https://brainly.com/question/19770987