I forgot how to solve for two variables... Please check if I solved both problems properly! Thank you.

Equations: (solve for t and z)
12t + 4z = 80
2t + 4z = 20

My answer: t = 2, z = 14

The steps:
(simplified it)
z = 20 - 3t, z = 5 - 0.5t
(equated both sides to isolate for t)
20 - 3t = 5 - 0.5t
t = 2
(sub t = 2 into one of the equations)
z = 20 - 3(2)
z = 14

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Equations: (solve for t and z)
z = 2 + 6t
z 20 - 3t

My answer: t = 2, z = 14
(I did the same steps like the previous question, my answer is kind of iffy because it's the same???)

Your answers are wrong.

20-3t=5-.5t does NOT come out t=2

redo that. Another quick way to do this is take your original equations, subtract the second from the first, and you get
10t=60 which is pretty fast to solve in your head.

To solve for two variables in a system of equations, you can use the method of substitution or the method of elimination. Let's go through the steps for both of the problems you provided.

Problem 1:
Equations:
12t + 4z = 80
2t + 4z = 20

Step 1: Simplify the equations
The second equation is already simplified, but let's simplify the first equation:
12t + 4z = 80

Step 2: Isolate one variable in terms of the other
Let's isolate t in the second equation:
2t + 4z = 20
2t = 20 - 4z
t = 10 - 2z

Step 3: Substitute the isolated variable into the other equation
Substitute t = 10 - 2z into the first equation:
12t + 4z = 80
12(10 - 2z) + 4z = 80
120 - 24z + 4z = 80
-20z = -40
z = 2

Step 4: Substitute the found value of z back into one of the equations to solve for t
Using the second equation:
2t + 4z = 20
2t + 4(2) = 20
2t + 8 = 20
2t = 12
t = 6

So, the correct solution is t = 6, z = 2.

Problem 2:
Equations:
z = 2 + 6t
z = 20 - 3t

Step 1: Simplify the equations (already done)

Step 2: Isolate one variable in terms of the other
Let's isolate t in the second equation:
z = 20 - 3t
3t = 20 - z
t = (20 - z)/3

Step 3: Substitute the isolated variable into the other equation
Substitute t = (20 - z)/3 into the first equation:
z = 2 + 6t
z = 2 + 6((20 - z)/3)
z = 2 + 12 - 2z
3z = 14
z = 14/3

Step 4: Substitute the found value of z back into one of the equations to solve for t
Using the second equation:
z = 20 - 3t
14/3 = 20 - 3t
3t = 20 - 14/3
t = (60 - 14)/9
t = 46/9

So, the correct solution is t = 46/9, z = 14/3 (approximately t = 5.11, z = 4.67).

Make sure to double-check these solutions and the calculations to ensure accuracy.