anyone good in math?

Question

i have to take a college placement test and i have not been back to school since 2001... i feel like i totally forgot math... anyone can help me out there... solve the system:
x - y = 1
3x + 4y = 24


order from smallest to largest: 0. 105, 0.501, 0.015, 0.15.


i just want to know how to solve this.. i want to have an understanding of it...

Answer 1

solve for x in the 1st equation.
x = 1 + y

Substitute 1 + y for the x in the second equation
3(1+y) + 4y = 24
3 + 3y + 4y = 24
3 + 7y = 24
7y = 21
y = 7

now we know y = 7, we can solve for x
x - y = 1
x - 7 = 1
x = 8

i think you know that 105 is greater than 0 and greater than fractions, and you know that fractions like .501 are greater than 0 and less then 1. So your prob. is to order 0.501, 0.015, 0.15

If you know that the numbers can be said as
.501 = 501/1000
.015 = 15/1000
.15 = .150 = 150/1000
I think you will agree that 501 thousandths is more than 150 is more than 15 thousandths

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Answer 2

1) First problem:

You can solve it using Gaussian reduction as follows.
x - y = 1...........(1)
3x + 4y = 24....(2)

Multiply (1) by 4 :

4x - 4y = 4 .........(1)
3x +4 y =24........(2)

Add (1) to (2):

4x+3x-4y+4y =4+24
7x+0 = 28
Solve for x:
x = 28 / 7 = 4

As you got x, you can substitute in the original (1):

(4) - y = 1 then solve for y:
-y =1-4
y=4-1
y=3

Hence, complete solution is x =4, y=3 (just check the result substituting in both equations. You have to get two identities)

2) Second problem:

In order to know what is the greatest and lowest values, just check where the decimal point is located in each number. The farthest to the left, the lowest the number is:

0.501>0.15>0.105>0.015

That's it!

Good luck!

Answer 3

x - y = 1 -> x = y + 1. Substitute into the second one:
3x + 4 y = 24 -> 3 ( y + 1) + 4 y = 24
-> 3 y + 3 + 4y = 24 -> 7 y = 24 -3 = 21 -> y = 3
x - y = 1, so x = 4.

Answer 4

to order the numbers multipy them then its easier to see. it becomes: 105, 501, 15, 150 (when multiplied by 1000 the decimal point moves to the right 3 digits because of the 3 zeros in 1"000" .....

for the system find x on one of the eq's: x-y=1 so x=1+y ... wirte x on the other system 3x+4y=24 so 3(1+y)+4y=24 3+3y+4y=24 so y=3 and so when put on any eq for instance the first: x-y=1 x-3=1 so x=4 :)

practice makes perfect

Answer 5

1. x - y = 1 and 3x + 4y = 24
*Solve for "x" or "y" in either equation. Let's solve for "x" in the 1st equation.

First: solve for "x" by isolating it on one side > add "y" to both sides (opposite sie means opposite sign) >

x - y + y = 1 + y
x = 1 + y

Sec: replace 1 + y with the "x" variable in the 2nd equation >

3(1 + y) + 4y = 24

*Use distribution to eliminate parenthesis > multiply 3 with both terms in the parenthesis >

3(1) + 3(y) + 4y = 24
3 + 3y + 4y = 24
3 + 7y = 24

*Solve for "y" > subtract 3 from both sides >

3 - 3 + 7y = 24 - 3
7y = 21

*Divide both sides by 7 >

7y/7 = 21/7
y = 3

Third: replace 3 with the "y" variable in the 1st equation >

x - 3 = 1

*Add 3 to both sides >

x - 3 + 3 = 1 + 3
x = 4

(4, 3)

Answer 6

solve one of the equations, for example
solve x-y = 1 ...so
add "y" to both sides.....and u get x=y+1
plug that into the other equation for "x"...so
3(y+1)+4y=24
distribute:
3y+3+4y=24
7y+3=24
subtract 3 to bothe sides
7y=21
divide by 7
y=3

now plug THAT into x-y=1 ( so you can slove for x)
x-3=1
x=4

(4, 3)


and the order: 0.015, 0.105, 0.15, 0.501

Answer 7

Another way to figure out system id elimination.
x-y=1
3x+4y=24

Take the x-y=1 and multiply it times 4 to one of them to where you can eliminate it.
4x -4y=4
3x+4y=24
now add them down
7x=28

the posative and negative y's cancell each other out.
Now divide by 7
7x=28
7 7

x=4

now take and put 4 in the original eqations to check. It must work with both or it isn't a good system

4-y=1
3(4)+4y = 24


4-(3)=1
12+4(3)= 24

It checks
x=4
y=3

Answer 8

X=4
y=3

You just substitute 0 for y to get X. And then substitute 0 in for x to get Y.

substitute 0 in for y
3x = 24
divide 3 from both sides
x=4

substitute 0 in for x
4y=24
divide 4 from both sides
y=3

Take your answers and substitute them back into the first equation.
x-y=1
4-3=1

if 4-3=1 is true (like in this case) your answers are correct and (x=4)(y=3)


smallest to largest
0.015
0.15
0.105
0.501

Answer 9

y = 3, x = 4

.015, .105, .15, .501


To solve a system of equations with two variables, you isolate one variable on one side of the equation like this:

x - y = 1

Add y to both sides and you get:

x = y + 1

then, in the second equation, put in (y +1) everywhere you see x.

3x + 4y = 24

3(y +1) + 4y = 24

Multiply it out:

3y + 3 + 4y = 24

add the like variables:

7y + 3 = 24

subtract 3 from both sides:

7y = 21

divide both sides by 7

y = 3

Now take the y = 3 and put it back in your original equation:

x - 3 = 1

add 3 to both sides

x = 4

Answer 10

To solve your system multiply the first equation by 4:
4x - 4y = 4
3x + 4y = 24

If you add these, the y's cancel, leaving
7x = 28
x = 4
Since x - y = 1,
x = 3

Second question: Say the numbers out loud
as thousanths and you will get
0.015 (= 15/1000)
0.105
0.150
0.501
as the order you need.