Help solve this Math equation please

So I'm doing test corrections for my Math, Algebra 2 with Geo. and I wasn't here half the year with a concussion, so I only had about 20 minutes to learn how to do most of these problems and I didn't do well.

So I'm supposed to write two eqations and solve them, to figure out how many pounds of peanuts (z) and how many pounds of cashews (x) go into making a 90 pounds mix, that he can sell for $270 (peanuts are $2.75 a pound, cashews are $5 a pound)

I got the two equations that he says is correct, but I have no idea how to solve them. They are :
270 = 5x + 2.75z and 90 = x + z.

How do I solve them? If it's the elimination method, I've searched that and I still can't figure out how to do it. Help is very much appreciated. Thanks!

Use elimination(or addition)

270 = 5x + 2.75z

90 = x + z

Multiply the second by -5 and add it to the first

270 = 5x + 2.75z

-450 = -5x -5 z
---------------------
-180= -2.25 z

z= -180/ -2.25

z=80

Substitute z in any of the equations to find x

90=x+80

x=10

use elimination. heres how:

Multiply the bottom x by -5 in order to eliminate the x values.

270 = 5x + 2.75z
90 = x + z * (-5)

now you have

270 = 5x + 2.75z
-450 = -5x -5z

Now elimate by adding equations:

270 5x 2.75z
-450 -5x -5z
-180= 2.25z

divide to find z

-180/2.25= 80 so z=80

plug in 80 for z

270 = 5x + 2.75(80) or 270 = 5x + 220
90 = x + (80) or 90 = x + 80

solve for x:

270- 220 = 50. 50/5= 10

x=10.

now you have the answer: x=10, z=80

using the elimination method, it will be like this
5x+2.75z=270
x+ z=90
5x+2.75z=270
-5x-5z=-450(multiple by -5)
-2.25z=-180