help with systems of equations?

Question

plz help me solve this using the substitution method:
3x+2z=1
5x+7z=20

this is as far as i got, x=(1-2z)/3

now what?

Answer 1

You would be much better off using the elimination method, but using the substitution method:
First you might want to write "x = (1 - 2z)/3" as "x = 1/3 - 2/3z"
Once you've done this plug this in to the other equation: 5x + 7z = 20... which gives you

5/1(1/3 - 2/3z) + 7z = 20

5/3 - 10/3z + 7z = 20...then convert 7z to 21/3z to get a common denominator so you can add the two like terms:

5/3 + 11/3z = 60/3...now subtract 5/3 from both sides:

11/3z = 55/3...now multiply both sides by 3/11 to get rid of the fraction next to z, leaving z by itself:

z = (55/3 x 3/11) = 5

Once you have z, plug it into the equation you first figured out:
x = 1/3 - 2/3z which gives you: x = 1/3 - 2/3(5)

...x = 1/3 - 10/3 = negative 9/3 = negative 3

Final Answer: z = 5, x = -3

Answer 2

ok so now that you have what x= for, then on the second equation put on every x what you have got, you should have something like this: 5(-2z+1/3) + 7z = 20, then you multiply and get the result which is a simple equation like this: -10/3z + 5/3 + 7z = 20. Move all the z to the left and all the numbers to the right to have this: -10/3z + 7z= 20 - 5/3. Then solve the equation and you'll get that z= 5. Then place on the first equation number 5 on every place you see z, to have something like this: 3x + 2(5) = 1. Solve this equation and you'll find out that x= -3. I hope that helped!!!

Answer 3

Now substitute

5x + 7z = 20
5((1-2z)/3) + 7z = 20

multiply out
(5-10z)/3 + 7z = 20

5/3 - 10z/3 + 7z = 20

Then just combine your z terms on the left and the non-z terms on the right

Then you can find z

Once you know z, substitue into one of the equations to find x

It is a good idea to substitue your z value into the second equation to verify that it is correct

Answer 4

okay its pretty simple... i just learned this in my algebra class...
multiply the whole top equation by 5 and the whole bottom equation by -3 you will end up with 15x + 10z= 5 and
-15x -21z= -60 then the 15 and -15 cancel out and you are left with 10z = 5 and -21z= -60 use subtraction to find those then you should end up with -11z= -55 then divide each side by -11 and z=5 then you "plug in" 5 for z and your equation should be 3x+2(5)=1 then you distribute and get 3x+10=1 then subtract 10 from each side and you should get 3x=-9 divide each side by 3 and x should equal -3 so your solution should be in coordinates and x comes before z so your solution is (-3,5)

Answer 5

now in the second equation
wherever you see x
put in what x equals