can someone help me with this math?

Question

it says
"use subituion to solve each system of equations. Check each by substituting it in both original equation"

1. a =3-b
4b+ a =15

2. x=2-y
8y+ x =16

3. even suggested solving problem 1 by substuting 3-b for a in the first equation Will evan's method work? explain why or why not.


uhmmcan you tell me how you solved the questions too/ please.

Answer 1

1. a =3-b ---(1)
4b+ a =15---(2)
from (2)--> 4b+(3-b)=15
4b+3-b=15
3b+3=15
3b=15-3
3b=12
b=12/3=4
apply the value of b in (1)---> a=3-(4)
a=-1
-------
2. x=2-y------(1)
8y+ x =16----(2)

from (2)---> 8y+(2-y)=16
8y+2-y=16
7y+2=16
7y=16-2
7y=14
y=14/7
y=2

apply the value of y in (1)
x=2-2=0

Answer 2

1. a =3-b
4b+ a =15

a=3-b thats what you substitute in 'a' for the next line
4b+ (3-b) =15

then you leave all variables on the left and numbers on the right
4b-b=15-3 (when you change sides on the = you change from + to - and viceversa )

that leaves you with 3b =12

then you solve that: b= 12/3 and this leaves you with b = 4

now in the original you put this and solve it
4(4) + a =15

16 + a =15 .... a = 15 -16 ..... a = -1
....................................................................................

2. x=2-y
8y+ x =16

you use the same method for this one giving x on the second line the value it states on the first line
8y + (2-y) =16
8y -y = 16-2
7y = 14
y=14/7
y= 2 now this value into the original

8(2) + x =16
16 + x =16
x = 16 - 16
x = 0
.................................................

ok its not that hard to understand this is the basics for all equations so i would suggest that you DO try to understand it, and maybe next time i wont have to do your homework. Just give some time, start with simple ones and a text book you can understand, then work your way up to harder ones, cause refusing to do it is only gonna make you fail math and physics and you need those clases to grad so, theres no way around it. Im not trying to lecture, i hope this helps, and you can almost always find your homework on the net ;) if you decide to go that way hehe , just make sure you start looking for it with enough times

Answer 3

1. 4b + (3-b) = 15
3b + 3 = 15
3b = 12
b = 4 <<
4(4) + (3-4) =15
16 -1 = 15

2. x = 2 - y
8y + x = 16

8y + 2 - y =16
7y + 2 =16
7y = 14
y = 2 <<<<<<
8(2) + 2 - 2 = 16
16 = 16

3. no it will not because you'll just end up with 3-b = 3-b and the b's will cancel which won't give you an answer.

Answer 4

a = 3-b, 4b + a = 15, substitute a =3-b in 4b + a = 15,which means 4b + 3 - b = 15, 4b - b = 15 - 3, 3b = 12, this means that b = 15 / 3, b = 5. this then means that a = 3 - 5 which is = -2

Answer 5

1. First substitute a for 3-b
4b+3-b=15
2. Subtract the like factors(b really = 1b) 4b-b
3. 3b+3=15
4. subtract 3 from each side(3b+3-3=15-3)
5. 3b=15
6. Divide 15 by 3 and you get b=5
Do the same steps for the second problem

Answer 6

1. "a = 3 - b" and "4b + a = 15"

First: replace "3 - b" with the a-variable in the 2nd equation....

4b + 3 - b = 15
3b + 3 = 15

Sec: subtract "3" from both sides....

3b + 3 - 3= 15 - 3
3b = 12

Third: isolate "b" on one side > divide both terms by 3....

3b/3 = 12/3
b = 4

Fourth: replace "4" with the b-variable in the 1st equation....

a = 3 - 4
a = -1

Solution: (-1, 4)


2. "x = 2 - y" and "8y + x = 16"

First: replace "2-y" with the x-variable in the 2nd equation....

8y + 2 - y = 16
7y + 2 = 16

Sec: subtract "2" from both sides....

7y + 2 - 2 = 16 - 2
7y = 14

Third: isolate "y" - divide both terms by "7"....

7y/7 = 14/7
y = 2

Fourth: replace "2" with the y-variable in the 1st equation....

x = 2 - 2
x = 0

Solution: (0, 2)

Answer 7

1) Since a = 3 - b, you can substitute (3-b) in for a.

4b + (3 - b) = 15
3b + 3 = 15
3b = 12
b = 4

a = 3 - 4
a = -1

2) Substitute (2 - y) in for x

8y + (2 - y) = 16
7y + 2 = 16
7y = 14
y = 2

x = 2 - 2
x = 0

3) As demonstrated above, it does work, since the values (3 - b) and a are the same.

Answer 8

1) 4b+3.-b=15
3b=12
b=4

a=3-4
a= -1


2) 8y+2-y=16
7y=14
y=2

x=2-2
x=0

3) no, because 3-b=3-b. everything cancel out and you left with 0=0 that means there is many solution but there's only 1 solution for this problem.

Answer 9

4b + 3-b = 15
3b = 12
b = 4

3 - 4 = a
a = -1

Answer 10

just plug in the entire value of a into the second equation, making the second equation:

4b+(3-b)=15

then just solve for b using algebraic methods.

once you have b you can plug tha value back into the first equation to solve for a. use the same method for the second equation, except be careful to watch for distribution after you substitute.