Two times a number plus ten times a second number is twenty. Thirty times the second number plus three times the first number is 45. What are the two numbers?

Question

How do I set my equations up? What are the answers?

Answer 1

you have two equations, you can solve by substitution or elimination.

equation 1 

2x + 10y = 20

equation 2

3x + 30y = 45

 

Substitution method:

2x +10y = 20      (divide both sides by 2)

(2x + 10y)/2 = 20/2

x + 5y = 10         

x = 10 - 5Y

3(10 - 5y) + 30y = 45   (substitute value of x from 1st equation)

30 - 15y + 30y = 45

15y = 15

y = 1

2x + 10y = 20

2x + 10(1) = 20

2x = 10

x = 5

verify

2x + 10y = 20

2(5) + 10(1) = 20

20 = 20

3x + 30y = 45

3(5) + 30(1) = 45

45 = 45

 

Elimination method:

2x + 10y = 20
3x + 30y = 45

 

(2x + 10y) * -3 = (20) * -3       

(3x + 30y) * 2 = (45) * 2

 

-6x - 30y = -60
6x + 60y = 90

 

-6x - 30y +6x + 60y = -60 + 90
30y = 30

y = 1

2x + 10y = 20

2x +10(1) = 20

2x = 10

x = 5