Linear equations

Question

One number is 5 less than 4 times another.If the sum of the two numbers is 11,find the numbers.

 

Answer 1

Let your numbers be represented by x and y

 

One number is 5 less than 4 times the other:

equation 1:  x = 4y - 5

 

The sum of the numbers is 11:

equation 2:  x + y = 11

 

Equation 1 already has solved for x in terms of y.

Substitute 4y - 5 in place of x in equation 2 and

solve for y

 

x + y = 11

4y-5+y = 11

5y-5 = 11  add 5 to both sides

5y = 16     divide both sides by 5

y = 16/5 = 3 1/5

 

Since x + y = 11 we have

x + 16/5 = 11

x = 11 - 16/5

x = 55/5 - 16/5

x = 39/5 = 7 4/5