Math question please help!!?

Question

This chapter is all about substitution, and i need a lot of help on this chapter! Please show me the steps to solve these systems. I just need some examples so i know how to do the rest I have left which is like 8 more problems. =p

1. x-3y=14
x-2=0

2. 2x+2y=5
y=1/4x

3. y=3
y=4/3x+2

4. 2y=o.2x+7
3y-2x=2

Answer 1

With solutions by substitution, you pick one equation and solve it for one variable, then plug that solution into the other equation. I'll give you the first two:

1) x - 3y = 14

x - 2 = 0

It doesn't matter which equation you solve, so I pick the one that looks like it'll work most easily. In this case, I'll solve the second one:

x = 2

Now plug that solution into the first equation:

x - 3y = 14
2 - 3y = 14
-3y = 12

y = -4

So your solution is x = 2, y = -4

2) This will be a little harder, but the same idea. You already have one equation solved for y, so use

y = (1/4)x

in the first equation

2x + 2y = 5

2x + 2(1/4)x = 5

2x + (1/2)x = 5

(5/2)x = 5

x = 5*(2/5) = 2

Now plug that into the first equation:

y = (1/4)x = (1/4)*2 = 1/2

So x = 2, y = 1/2

Hope that helps.

Answer 2

x-3y = 14
x -2 = 0

If you look at the second equation you know x = 2
Substitute x =2 into the first equation you have

2 - 3y = 14
-3y = 12
y = -4

***

2x + 2y = 5
y = (1/4) x

Use the second equation y = 1/4x and substitute 1/4x into eqaution1 for every y

2x + 2[(1/4)x] = 5
2x + (1/2)x = 5
4x + x = 10 (multipled each side by 2 just for easy math)
5x = 10
x = 2

Then back to equation 2 you have
y = (1/4)x

but since x = 2 by substitution you have

y = (1/4)2
y = 2/4
y = 1/2

*****
OK you have the idea, I won't be so wordy...

y = 3
y = 4/3x + 2

3 = 4/3x + 2
9 = 4x + 6 (mutiply each side by 3)
3 = 4x
3/4 = x

****

2y = .2x + 7
3y - 2x = 2

equation1
2y = .2x + 7
y = .1x + 7/2

equation 2
3y - 2x = 2
3 (.1x + 7/2) -2x = 2
.3x + 21/2 -2x = 2
3x + 105 - 20x = 20 (multiply each side by 10)
-17x = -85
x = 5

If x = 5 then in equation #2 we have
3y - 2x = 2
3y - 2(5) = 2
3y - 10 = 2
3y = 12
y = 4

Answer 3

1. Solve one equation for a single variable
x-2=0
x=2 as in the second equation
Substitute that into the other equation an solve
(2)-3y=14
-3y=12
y=-4
Once you solved for the variable substitute it into the equation and solve for the other
x-3(-4)=14
x+12=14
x=2
So x=2 and y=-4

Same thing with the others

Answer 4

okay, here we go:

1) start by solving for X in the second problem:
x-2=0.
x-2+2 = 0+2
x = 2
then plug that answer into the first problem:
x-3y=14
2-3y = 14
2-2-3y = 14-2
-3y = 12
y = 12/-3
y = -4 <-- your answer

2) We'll start on the second equation here as well:
y=1/4x
4y=x
x=4y
plug that into the first equation and you get:
2x+2y=5
2(4y)+2y=5
8y+2y=5
10y=5
y = 1/2 = .5 <--- your answer

3) we'll start with the first equation here, since it's already solved.
y=3
plug that into the second equation and you get:
y=4/3x+2
3=4/3x+2
3*3=(4/3x*3)+(2*3)
9=4x+6
9-6=4x+6-6
3=4x
3/4=4x/4
x = 3/4 = .75 <--- your answer

4) this one is a little trickier, if you solve the first equation first, you end up with nasty decimals (darn you 0.2x!), if you solve the second equation first you end up with fractions (darn YOU 3y!). I'm better with fractions, so I'm going to solve the second first:

3y-2x=2
3y-2x+2x=2+2x
3y=2x+2
y=2/3x+2/3

plug that into the first equation:

2y=0.2x+7
2(2/3x+2/3) = 0.2x+7
4/3x+4/3 = 1/5x+7

I'll put the fraction in equal terms:

20/15x+20/15=3/15x+105/15
20/15x-3/15x+20/15 = 3/15x-3/15x + 105/15
17/15x+20/15 = 105/15
17/15x+20/15-20/15 = 105/15-20/15
17/15x = 85/15
17/15x*15 = 85/15*15
17x = 85
17x/17=85/17
x = 5 <-- your answer

Answer 5

very simple:

just plug in x or y for whichever problem they are asking for.
once you get the hang of it, it's very easy to do.

1. x-2=0
add 2 to 0 so it looks like this --> x=2
then plug it into the equation x-3y=14
(2)-3y=14
-2 from 14
so -3y=14+2
-3y=16
divide 16 by -3 and there's your
answer.

hope it helps--i'm no math major :)

Answer 6

1) x-3y=14
x-2=0
+2 +2
x=2

2-3y=14
-2 -2
-3y/-3= 12/-3
y=-4

2) 2x+2y=5
y=1/4x

2x+2(1/4x)=5
2x+.5x=5
2.5x=5
2.5x/2.5=5/2.5
x=2

y=1/4x
y=1/4(2)
y=1/2

3) y=3
y=4/3x+2

3=4/3x+2
-2 -2
(3/4)1=4/3x(3/4)
3/4=x

4)
2y=0.2x+7
3y-2x=2

2y/2=.2x+7/2
y=.1x+3.5

3(.1x+3.5)-2x=2
.3x+10.5-2x=2
-1.7x+10.5=2
-10.5 -10.5
-1.7x=-8.5
-1.7x/-1.7=-8.5/-1.7
x = 5
y=.1x+3.5
y=.1(5)+3.5
y=.5+3.5
y=4

Answer 7

If I could I would send all these answerers a brand new roll of Duct tape, they helped this youngster with a problem. Without all the sarcasm of do it yourself.... I have a renewed belief that some are actually helped on this site