Find the numbers.

Question

A first number plus twice a second number is 17. Twice the first number plus the second totals 19. Find the numbers.

Answer 1

f = first number

s = second number

 

f + 2s = 17

2f + s = 19                  Solving the system by substitution or elimination. I'll do substitution.

 

f = 17 - 2s

2(17 - 2s) + s = 19

34 - 4s + s = 19

-3s = -15

s = 5

 

f + 2(5) = 17

f + 10 = 17

f = 7

Answer 2

Let x = first number

Let y = second number

 

x+2y=17

2x+y=19

 

We end up with a system of equations.

 

Now we multiply the first equation by 2 and subtract the both equations.  This will allow you to solve for y.  After you have y, chose any equation and substitute that value for y.  Now solve for x.