solve linear equation question for me...?

Question

2k + 3h = 8
5k - 2h = -18
find the value of k and h.

i could'nt understand my maths teacher....
heard there's 2 ways 2 find 'em(k & h)
do tell me both
please show the full calculation 4 me!!!!

Answer 1

What you want to do is solve one equation for one variable and substitute for it in the other.

So using the first equation

2k+3h = 8
2k = 8 - 3h
k = 4 - 3h/2

We solved for k in terms of h. Now substitute that into the second equation.

5k - 2h = -18
5(4 - 3h/2) - 2h = -18

Since this is an equation only in h, you can solve this equation for h.

20 - 15h/2 - 2h = -18
20 - 15h/2 - 4h/2 = -18
20 - 19h/2 = -18
19h/2 = 20 +18 = 38
h = 38*2/19 = 4

so h=4

You can subsititute this into any equation to solve for k.

2k + 3h = 8
2k + 3(4) = 8
2k + 12 = 8
2k = -4
k = -2

So k=-2 and h=4 is the solution.

Answer 2

Elimination by addition Method

2k + 3h = 8- - - - - - - -Equation 1
5k - 2h = - 18- - - - - - Equation 2
- - - - - - - - - - -

Multiply equation 1 by 2 and equation 2 by 3

2k + 3h = 8

2(2k) + 2(3h) = 2(8)

4k + 6h = 16

- - - - - - -

5k - 2h = - 18

3(5k) - 3(2h) = - 3(18)

15k - 6h = - 54

- - - - - - - - - --

Elimination of h

4k + 6h = 16
15k - 6h = - 54
- - - - - - - - - -

19k = - 38

19k / 19 = - 38 / 19

k = - 38/19

k = - 2

Insert the k value into equation 1
- - - - - - - - - - - - -

2k + 3h = 8

2( - 2) + 3h = 8

- 4 + 3h = 8

Transpose 4

- 4 + 3h + 4 = 8 + 4

3h = 12

Divide both sides of the equation by 3

3h / 3 = 12 /3

h = 12/3

h = 4

Insert the h value into equation 1

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

Check for equation 1

2k + 3h = 8

2(- 2) + 3(4) = 8

- 4 + 12 = 8

8 = 8

- - - - - - - - - - -

Check for equation 2

5k - 2h = - 18

5(- 2) - 2(4) = - 18

- 10 - 8 = - 18

- 18 = - 18

- - - - - - - - - --

Both equations balance

k = - 2

h = 4

- - - - - - - -s-

Answer 3

First way:

you isolate k in the first equation k = 4 - 3h/2

Substitute K in the second equation: 5(4-3h/2) - 2h = -18

Now solve the last: 20 - 15h/2 - 2h = -18 ==> -19h/2 = -38

==> h = 4 .... replace h by 4 in k= 4 - 3h/2
and find k = 4 - 3(4)/2 = -2

solution: h=4 and k = -2


Second way:
Multiply the first equation by 5 and the second by -2 and add the equations:

10k + 15h = 40 and -10k +4h = 36....

Adding we get 19h = 76 ==> h = 4

Now replace h=4 in the first equation: 2k + 3(4) = 8 and isolate k .... 2k = 8 - 12 ==> 2k = -4 ==> k = -2

There are other ways...

Answer 4

this is simultaneous equations and they can be solved graphically, but substitution or by elimination. It's usually easiest to solve them by elimination but it sound like you may have been asked to draw them on a graph (graphically)

you need to draw both of these lines on a graph and note where they cross and this will give you the values for k & h.

by elimination:

2k + 3h = 8
5k - 2h = -18

lable the top one as one and the bottom one as two

you need to find a common value of either k or h so to do this you'll need to multiply one by 2 and two by 3 to get:

4k + 6h = 16
15k - 6h = -54

The two h values are now both 6 it doesn't matter that one is - and the other is +

The rule you need to remember is SAME SIGN SUBTRACT

which applies here so you must minus eqtn 2 from eqtn 1

to get:

-11k = -38
you can multiply these by -1 to get:

11k = 38

then divide 38 by 11

k= 3 5/11 (easier to keep in fractions)

then sub this into eqtn 1

2k + 3h = 8
6 10/11 + 3h = 8
3h = 1 1/11
h = 4/11

to check this sub these values into eqtn 2

5k - 2h = -18
17 3/11- - 8/11 = 18

because there are two - signs you must add these values

this gives you 18

Answer 5

The two methods are substitution and addition.

Substitution:
Since 2k+3h=8
k=(8-3h)/2
now replace k from the second equation with (8-3h)/2
and we get
5*(8-3h)/2 - 2h = -18
this is a simple equation and the solution is h= 4
so k = -2

Addition
Multiply the first equation by 2 and the second by 3 we get:
4k + 6h = 16
15k - 6h = -54
Now add these equations together we get
19k + 0h = -38
so k = -2
now use this to solve either of the others and get h=4

Answer 6

Yes, there are two basic methods to do it. I'll only show one method since the second method is pretty long and boring one. Haha. Well, here's how it goes:

2k + 3h = 8
5k - 2h = -18

Mark any of the equation as "1" and the other as "2". We do as:
2k + 3h = 8 ----------1
5k - 2h = -18 ----------2

Out of two unknowns, h and k, write one in terms of other using any of the two equtions. We use equation 1 and make k the subject of equation. So equation 1 becomes:

k = (8 - 3h)/2

Call it equation 3.

k = (8 - 3h)/2 ----------3

Substitute this value of k in equation 2. So equation 2 becomes:

5(8 - 3h)/2 - 2h = -18

Simplying it becomes:

40 - 15h - 4h = -36

-19h = -76
h = 4.

Substitue this value of h in equation 3 to obtain the value of k:

k = (8 - 3h)/2 = (8 - 3*4)/2 = (8 - 12)/2 = -4/2 = -2

So: h = 4 & k = -2

Answer 7

2k +3h = 8
5k - 2h = -18
=
7k + h = -10
h = -10 -7k

2k +3(-10 -7k) = 8
2k -30 - 21k = 8
-19k -30 = 8
-19k = 38
k = -2

2(-2) +3h = 8
3h = 12
h = 4

Answer 8

you could the two use substitution or removal. Substitution: a million)remedy one equation for y so as which you have in ordinary terms one variable to remedy for: y=2-7x 2) Now, understanding what y equals, plug the value in to the subsequent equation so as which you have 5x+2(2-7x)=4 3) Now remedy for x. the respond is x=0 4) Now plug x decrease back into the 1st equation to discover y. the respond is y=2 5) Now plug in the two your values to the two your equations to make certain if the values are dazzling. _____________________________________ removal: a million) Multiply the full first equation via -2 so as which you will cancel out the y's. this materials: -14x-2y=-4 5x+2y=4 2) Now cancel out the y's via including the two equations. This leaves you with: -11x=0 3) remedy for x and discover that x=0 4) Plug your x fee into one equation to discover the value of y. 5) 7(0)+y=2, so y=2 6) Plug on your 2 variables x=0 and y=2 into the two equations to ascertain that your values are dazzling.

Answer 9

2k + 3h = 8 (x5)
5k - 2h = -18 (x2)

10k = 15h = 40
10k - 4h = -36

19h = 76, h=4

2k + 12 = 8, 2k = -4, k = -2

5k -8 = -18, 5k= -10, k = -2

Answer 10

Multiply the first equation by 2 and the second by 3.
4k+6h=16
15k-6h=-54
Add
19k=-38
k=-2
At this point you could substitute -2 for k in either equation and find h.
OR Another way:
Multiply the first equation 5 and the second by -2
10k+15h=40
-10k+4h=36
Add
19h=76
h=4
and then substitute 4 for h in either equation and find k.