SOLUTION: Y=-2x+4 Y-3x=-11 How do you substitue this? I also have a problem that I cant figure out but if you cant help thats fine. "The product of two numbers is 60. One number exceed

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Question 1101744: Y=-2x+4
Y-3x=-11
How do you substitue this?
I also have a problem that I cant figure out but if you cant help thats fine.
"The product of two numbers is 60. One number exceeds another by 7. Find the two numbers."
Found 4 solutions by stanbon, Alan3354, richwmiller, josgarithmetic:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Y=-2x+4
Y-3x=-11
How do you substitue this?
------
-2x+4 = 3x-11
5x = 15
x = 3
---------------------
I also have a problem that I cant figure out but if you cant help thats fine.
"The product of two numbers is 60. One number exceeds another by 7. Find the two numbers."
x + y = 60
x - y = 7
------
2x = 67
x = 33.5
y = 26.5
------------
Cheers,
Stan H.
------------
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
"The product of two numbers is 60. One number exceeds another by 7. Find the two numbers."
=============
Use trial and error.
Try pairs of factors of 60 to find a pair that differ by 7.
-----
1*60 NG
2*30 NG
etc
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
The product =60 not the sum
(x-7)*x=60
x^2-7x-60=0
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .



Now multiply the first coefficient by the last term to get .



Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?



To find these two numbers, we need to list all of the factors of (the previous product).



Factors of :

1,2,3,4,5,6,10,12,15,20,30,60

-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60



Note: list the negative of each factor. This will allow us to find all possible combinations.



These factors pair up and multiply to .

1*(-60) = -60
2*(-30) = -60
3*(-20) = -60
4*(-15) = -60
5*(-12) = -60
6*(-10) = -60
(-1)*(60) = -60
(-2)*(30) = -60
(-3)*(20) = -60
(-4)*(15) = -60
(-5)*(12) = -60
(-6)*(10) = -60


Now let's add up each pair of factors to see if one pair adds to the middle coefficient :



First NumberSecond NumberSum
1-601+(-60)=-59
2-302+(-30)=-28
3-203+(-20)=-17
4-154+(-15)=-11
5-125+(-12)=-7
6-106+(-10)=-4
-160-1+60=59
-230-2+30=28
-320-3+20=17
-415-4+15=11
-512-5+12=7
-610-6+10=4




From the table, we can see that the two numbers and add to (the middle coefficient).



So the two numbers and both multiply to and add to



Now replace the middle term with . Remember, and add to . So this shows us that .



Replace the second term with .



Group the terms into two pairs.



Factor out the GCF from the first group.



Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.



Combine like terms. Or factor out the common term



===============================================================



Answer:



So factors to .



In other words, .



Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
--------------------------------------------
Y=-2x+4
Y-3x=-11
How do you substitue this?
------------------------------------------

How to substitute is obvious.



----------------------------------------------
I also have a problem that I cant figure out but if you cant help thats fine.
"The product of two numbers is 60. One number exceeds another by 7.
----------------------------------------------




-

but instead of trying to solve as quadratic equation, you might also try to factorize 60 and look for any combination whose difference is 7.
Any?
----------Maybe the last one?




The two numbers are 5 and 12.
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