Question

Find the numbers whose sum in 13, if three times the first number is increased by four times the second number equals 32

Answer 1

First number = x

Second number = y

the sum of both numbers is 13:

x+y=13 (a)

if three times the first number is increased by four times the second number equals 32

3x+4y=32 (b)

We have the system of equations:

x+y=13 (a)

3x+4y=32 (b)

Solve (a) for x:

x=13-y

Replace x in (b)

3 (13-y)+4y= 32

Solve for y

3 (13)+3(-y)+4y=32

39-3y+4y=32

39+y=32

y=32-39

y= -7

Replace y on (a)

x+(-7)= 13

x=13+7

x= 20

First number =20

Second number = -7