systems of equations: subtitution. x=y+8 4x+2y=2, a=-3b a+5b=14, 2m-n=4 n=m-1?

Question

need to solve the equations by substitution. there is two problem to subtitution, solve each system sing the subtitution methond.

Answer 1

1. 4x+2y=2
4(y+8)+2y=2
4y+32+2y=2
6y+(32-32)=2-32
6y=-30
6y/6=-30/6
y=-5

2. a=-3b
a+5b=14
(-3b)+5b=14
2b=14
b=7

3. 2m-n=4
2m-(m-1)=4
2m-m+1=4
m=3

subsititue the variables back into the equation to find the second variable

Answer 2

since x=y+8, 4(y+8)+2y=2 so 4y+32+2y=2 so 6y=-30 so y=-5
if y=-5, substitute that back into the first one, x=y+8
so x=-5+8 -5+8 is the same as 8-5 so x=3
x=3 y=-5

using the same concept, if a=-3b, then a+5b=14 is the same as -3b+5b=14, so 2b=14 so b=7
if b=7, sub it back in so a=-3(7) so a=-21
a=-21 b=7

once again
if n=m-1 then 2m-n=4 is the same as 2m-(m-1)=4
so 2m-m+1=4 so m+1=4 so m=3
if m=3, and n=m-1 3-1=2 so n=2
m=3 n=2

Answer 3

I'm guessing the equations come in pairs.

1. x=y +8 and 4x + 2y=2

x=y + 8
Take y + 8 and substitute in second equation where x is.

4 (y+8) +2y=2
Distribute.

4y + 32 + 2y=2.
Combine like terms.

6y +32=2.
Subtract 32 from both sides.

6y= -30
y= -5


2. a= -3b and a+5b=14

Substitute -3b in second equation where a is.

(-3b) + 5b =14
Combine like terms.

2b=14
b=7


3. 2m-n=4 and n=m-1

Substitute m-1 in first equation where n is.

2m - (m-1)=4
Distribute.

2m -1m +1=4
Combine like terms.

m+1=4
Subtract 1 from both sides.
m=3


When there are two or more equations, look for one that already isolates a variable.

Answer 4

4(y+8)+2y=2
4y+32+2y=2
6y+32=2
6y+32-32=2-32
6y=-30
y=-5

-3b+5b=14
2b=14
b=7

2m-m-1=4
m-1=4
m+1-1=4-1
m=3