Substitution and Eliminating Variables???

Question

Time ran short in class and the class couldn't get all the notes about this stuff so i gotta problem like this...

2x+y=1
{
10x-4y=2

how the heck do i do all this??
help please??
much appreciation!!!!!!

Answer 1

2x+y=1

y=1-2x

10x-4(1-2x)=2

10x-4+8x=2

10x+8x=2+4

18x=6

x=1/3

y=1-2(1/3)

y=1-2/3

y=1/3

check:

2(1/3)+1/3=1

Answer 2

well there are 2 ways you can do it. one is to make one of the variables equal so you can eliminate it, or the other is to solve for a variable and use that in the other equation. here:

~making one variable equal so it cancels out:
2x+y=1
{
10x-4y=2
multiply the first sentence through by 4.
so you have:
8x+4y=4 (dont forget: multiply all by 4, not just the variables)
10x-4y=2 (notice how now you have 4y and -4y)
so add them and you get:
18x=6
so you get:
x=6/18 or 1/3
now substitute back in for x 1/3 to find y: 2x1/3+y=1
2/3+y=1
y=1/3.

other way: solving for a variable and substituting it in
so lets take the first equation:
soving for y:
subtract 2x from 1 side, so you get:
y=1-2x
so substitute that into the equation:
10x-4(1-2x)=2
10x-4+8x=2
so then you get, 18x-4=2
then by solving with simple algebra,
you get 18x=6
x=1/3
now substitute back in:
10x1/3-4y=2
3 1/3-4y=2
-4y=4/3
y=1/3.
voila! lol
hope that helps!!!

Answer 3

I - (2x+y=1
II -(10x-4y=2

Equation I:
y = 1 - 2x
Substitution y
Equation II:
10x - 4(1-2x) = 2
10x - 4 +8x = 2
18x = 2 + 4
x = 6/18
x = 1/3
Substitution of x:
y = 1 - 2x
y = 1 - 2(1/3)
y = 1 - 2/3
y = 1/3
Solution: {x, y elements of R | x = y = 1/3}
<>

Answer 4

Substitution Method

2x + y = 1
10x - 4y = 2

2x + y = 1
y = -2x + 1

10x - 4(-2x + 1) = 2
10x + 8x - 4 = 2
18x = 6
x = (1/3)

y = -2(1/3) + 1 = (-2/3) + 1 = (-2 + 3)/3 = (1/3)

ANS : ((1/3),(1/3))

-----------------------------------------

Elimination Method

2x + y = 1
10x - 4y = 2

Multiply top by 4

8x + 4y = 4
10x - 4y = 2

18x = 6
x = (1/3)

2(1/3) + y = 1
(2/3) + y = 1
y = 1 - (2/3)
y = (3 - 2)/3
y = (1/3)

ANS : ((1/3),(1/3))

Answer 5

1)pick an equation and sole for a letter:
y=-2x+1
2)substitute -2x+1 into the second equation replacing y:
10x-(-2x+1)=2
3)solve for remaining letter:
x=4
4)replace answer back int step 1 to solve for y:
y=-2(4)+1 y=-7
5)write answer in point form:
(4,-7)