SOLUTION: Find two numbers such that their sum is 12 and two times the first plus three times the second is 26

Question 57035This question is from textbook Algebra 2 with trigonometry
: Find two numbers such that their sum is 12 and two times the first plus three times the second is 26 This question is from textbook Algebra 2 with trigonometry

Found 2 solutions by susie, venugopalramana:
Answer by susie(3) (Show Source): You can put this solution on YOUR website!
use x to represent the first #
use y to represent the second #
then set up equations
x + y = 12 (sum means to add)(is means equal to)
2x + 3y = 26 (times means to multiply)
then you can multiply the first equation by -2 to isolate y
-2 (x + y = 12) = -2x - 2y = -24 (then add the second equation)
+ 2x + 3y = 26 (the x's are cancelled out)
-----------------
y = 2 (plug it in to the first equation to find x)
x + 2 = 12
- 2 -2
------------
x = 10 (you can plug in your answers to the original problem to double check yourself)

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Find two numbers such that their sum is 12 and two times the first plus three times the second is 26
LET THE 2 NUMBERS BE X AND Y
THEIR SUM = X+Y = 12....................................I
2 TIMES I NUMBER = 2X
3 TIMES II NUMBER = 3Y
THEIR SUM IS..... 2X+3Y = 26................................II
EQN.II - 2*EQN I
2X+3Y-2X-2Y=26-2*12=26-24=2
Y = 2
X = 12-2 = 10
SO THE 2 NUMBERS ARE 10 AND 2
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