10 POINTS!!!! i need algebra 1+2 help. it's on problem solving using two varibles.?

Question

how do do this problem. could you answer it step by step

the difference in two numbers is 7. two times the larger number,decreased by 3 times the smaller number, is 5. Find the two numbers.

the answer 5.3 and 3. is that right?

Answer 1

Let the numbers be a and b, where a>b

"the difference in two numbers is 7" tells you:
a - b = 7 or a = b+7

"two times the larger number,decreased by 3 times the smaller number, is 5" tells you
2a-3b=5

Plugging the first equation into the second gives you:
2(b+7) - 3b = 5
14 - b = 5
b = 9

so a = 9+7 = 16

Answer 2

no, that isn't right. First you have to turn the words into an equation.

So the difference in the two numbers is 7. Say X is the larger number and Y is the smaller number.

X-Y=7. So you can solve for X and X=Y+7

Now, the second equation says that the larger number times 2, minus the smaller number times 3 equals 5.

So the equation is 2X-3Y=5.

Since you solved for X in the first equation, plug this value into the X of the second equation. 2(Y+7) - 3Y = 5

Now solve for Y.
2(Y+7) - 3Y = 5
2Y + 14 - 3Y = 5
14-Y = 5
9 = Y

Now that you know Y, solve the first equation, and that will give you the value of X.
X - Y = 7
X- 9 = 7
X= 16.

Y is equal to 9, and X is equal to 16.

Answer 3

In reality, you don't need two variables, just designate each number as described in the problem.

We have this number, lets call it x
We have a second number that is 7 less than x, we can write it as x-7.

Then write an equasion based on what is stated in the problem with these two numbers...

2x-[3(x-7)]=5

then solve for x

2x-3x+21=5
-x=-16
x=16

If x=16, then the other number is 7 less, or 9

Youcan see if this is correct by doing the following...
Does 2 times 16 minus 3 times 9 equal 5??

Answer 4

first you write it out. so, X-Y=7 and 2x-3y=5. then u can either use substitution, or elimination. here is substitution: X=Y+7 so, take the second equation and plug in X. like so: 2(Y+7)-3Y=5 then distribute it.....2Y+14-3Y=5.....-Y=-9 then times by -1 so Y=9. THEN PLUG IN Y INTO THE FIRST EQUATION, and you get this: X-9=7 so X=16. SO the answer is X=16 AND Y=9. hope this helps! :-)

Answer 5

the difference in two numbers is 7 is : A minus B equals 7
two times the larger ... is: 2A minus 3B equals 5

therefor

A - B plus 2A - 3B = 5 + 7

I hope that's enough to get your own brain working with what you've been taught so far as it's useless for others to give you complete answers . you won't learn that way, how to do it yourself. Get out your text book and read the instructions over and over until you understand more and more .. it will come with patience and persistance.

Answer 6

1. Form your system of equations. F=First number and S=second number (I just chose those variables so I can remember). The difference is 7 can be expressed as

F-S=7

2 times the larger number (the first one obviously, as specified above) - 3 times the small number (S)=5

2F-3S=5

Now we have

F-S=7
2F-3S=5

You have to balance them, so you can multiply the top by 2. Then solve.

2F-2S=14
- 2F-3S=5
------------
0F+ 1S= 9
S=9

Plug that into our equation to find F.

F-(9)=7
F=16

Therefore

F=16 and S=9

Answer 7

-->rewrote to make sparkling negatives: 2x + 4y + -5z = -10 -1x + -2y + 8z = 16 -2x + 4y + 2z = 4 because 2x and -2x already get rid of one yet another, upload them mutually (ignore concerning the ....): ..2x + 4y + -5z = -10 -2x + .4y + .2z = ...4 ---------------------------- .........8y + -3z = -6 (>>you're keeping the 2d equation: you purely used it to get rid of a variable>>) which resources: ..........8y + -3z = -6 -1x + -2y + 8z = 16 -2x + 4y + ..2z = 4 -->I nonetheless want to get rid of yet another x, so i'm able to multiply the 2d equation through 2: -2(-1x + -2y + 8z = 16) 2x + 4y + -8z = -32 upload to third equation: ..2x + 4y + -8z = -32 -2x + 4y + 2z = 4 ---------------------- ...........8y + -6z = -28 this resources: ..........8y + -3z = -6 ..........8y + -6z = -28 -2x + 4y + 2z = 4 -->i'm able to diminish this equation to a lot less stressful numbers through dividing each and every time period on each and each section through 2: -1x + 2y + z = 2 now, i exploit the first 2 equations to get rid of one y time period: -a million(8y + -3z = -6) -8y + 3z = 6 upload to 2d equation: -8y + 3z = 6 8y + -6z = -28 --------------------- ........-3z = -22 My device of equations is now: .........8y + -3z = -6 .................-3z = -22 -1x + 2y + z = 2 to unravel the device of equations: ascertain for z: -3z = -22 z = -22/-3 = 22/3 -->i am going to leave in fraction style for now use z = 22/3 and ascertain for y: 8y + -3*22/3 = -6 8y + -22 = -6 8y = -6 + 22 8y = 16 8y/8 = 16/8 y = 2 use z=22/3 and y=2 to unravel for x: -1x + 2y + z = 2 -1x + 2*2 + 22/3 = 2 -1x +4 + 22/3 = 2 -->replaced all finished numbers to thirds: -1x + 12/3 + 22/3 = 6/3 -1x + 34/3 = 6/3 -1x = 6/3 + -34/3 -1x = -28/3 x = 28/3 x = 28/3 y = 2 z = 22/3