Answer:
The solution is x=1,y=2,z=3
Step-by-step explanation:
The given system of equations is ;\
2x−3y+4z=8...(1)
3x+4y−5z=−4...(2)
4x−5y+6z=12...(3)
Make x the subject in equation (1)

Put equation (4) into equation (2) and (3)

Multiply through by;

Expand;

Simplify;

Equation (4) in (3)





Put equation (6) into equation (5)




z=3
Put z=3 into equation (6)
y=2(3)-4=2
Put y=2 and z=3 into equation 4

The solution is x=1,y=2,z=3
There would be 100,000 if there are no restrictions on the digits and 90,000 if they cannot use 0 as the first digit.
If there are no restrictions, there are 10 possibilities for each digit:
10(10)(10)(10)(10) = 100,000
If the first digit cannot be 0, there are 9 possibilities for it and 10 possibilities for each of the other 4:
9(10)(10)(10)(10) = 90,000
Option A:

Solution:
ABCD and EGFH are two trapezoids.
To determine the correct way to tell the two trapezoids are similar.
Option A: 
AB = GF (side)
BC = FH (side)
CD = HE (side)
DA = EG (side)
So,
is the correct way to complete the statement.
Option B: 
In the given image length of AB ≠ EG.
So,
is the not the correct way to complete the statement.
Option C:
In the given image length of AB ≠ FH.
So,
is the not the correct way to complete the statement.
Option D:
In the given image length of AB ≠ HE.
So,
is the not the correct way to complete the statement.
Hence,
is the correct way to complete the statement.
A two digit number has a tens digit and a ones digit.
Let's say x = tens digit and y = ones digit
"The sum of the digits is 5"
x + y = 5
The next phrase is "the number multiplied by 3 is 42" but we need to represent the number using the digits. So they need to be multiplied first by their place value and added together. [Example: 34 = 3(10) + 4(1)]
The number is: 10x + y
3(10x + y) = 42
The system of equations: (two equations for two unknowns)
x + y = 5
30x + 3y = 42
Then you can use substitution or elimination to combine and solve.
I'll use elimination, multiply the entire top equation by -3 and add the equations together. y will cancel out
-3x - 3y = -15
30x + 3y = 42
------------------
27x + 0 = 27
x = 1
then plug x = 1 into either equation to find y
1 + y = 5
y = 4
remember the x and y represent digits so the number xy is 14