SOLUTION: Seven times the larger number is 8 more than four times the smaller. Also, three times the smaller is 19 less than twice the larger. What are the numbers?

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Question 65599This question is from textbook An Incremental Development
: Seven times the larger number is 8 more than four times the smaller. Also, three times the smaller is 19 less than twice the larger. What are the numbers? This question is from textbook An Incremental Development

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= smaller number
And y=larger number
Now we are told that seven times the larger number (7y) is 8 more that 4 times the smaller number (4x). So we have
(1) 7y-8=4x one of our equations
We are also told that three times the smaller number (3x) is 19 less than twice the larger number (2y). And we get:
(2) 3x+19=2y our second equation
Our drill is to solve:
(1) 7y-8=4x
(2) 3x+19=2y
rearranging, we have:
(1)4x-7y=-8
(2)3x-2y=-19
Multiply (1) by 3 and (2) by 4 and we get:
(1)12x-21y=-24
(2)12x-8y=-76
Subtract (2) from (1) and we have:
0-13y=52
y=-4 larger number
Substitute y=-4 in (1)
4x+(7)(4)=-8
4x+28=-8
4x=-28-8=-36
x=-9 smaller number
Ck
substitute in (1) and (2)
(1) 7y-8=4x =7(-4)-8=4(-9)
-36=-36
(2) 3x+19=2y =3(-9)+19=2(-4)
-8=-8
Hope this helps----ptaylor