SOLUTION: Please help me solve this, im confused The difference between the first number and two times the second number is -54, while the sum of three times the first number plus

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Question 1044135: Please help me solve this, im confused

The difference between the first number and two times the second
number is -54, while the sum of three times the first number plus
twice the second is 94. What is the first number?
Found 2 solutions by Boreal, ankor@dixie-net.com:
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
the numbers are x and y
x-2y=-54 (difference means subtraction)
3x+2y=94
now add the two equations because the y's will disappear
4x=40
x=10
substitute into the first equation
10-2y=-54
-2y=-64
y=32
check with the second equation (or vice versa)
30+64=94
Now answer the question.
The first number is 10.

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
let a = the 1st number
let b = the 2nd number
:
Write an equation fore each statement
:
The difference between the first number and two times the second
number is -54,
a - 2b = -54
:
while the sum of three times the first number plus twice the second is 94.
3a + 2b = 94
:
use elimination on these two equation
a - 2b = -54
3a + 2b = 94
--------------Addition eliminates b, find a
4a = +40
a = 40/4
a = 10
:
Use the 1st equation to find b
10 - 2b = -54
-2b = -54 - 10
-2b = -64
b = -64/-2
b = +32
:
;
Check solutions in the 2nd equation
3(10) + 2(32) = 94
30 + 64 = 94