Question

X-2*a=30 2*z+y=30 6*z=30 2*y-a=30 f+3*z=30

Answer 1

Z = 30/6 = 5
y = 30-2z = 30-2*5 = 20
a = 2y - 30 = 2*20-30 = 10
x = 30+2a = 30+2*10 = 50
f = 30-3z = 30-3*5 = 15

Answer 2

To solve this system of equations for the variables a, y, z, and f, we can use the method of substitution or elimination. Let's use the elimination method to simplify the equations and find the values of the variables:

Here are the equations:

1. X - 2*a = 30
2. 2*z + y = 30
3. 6*z = 30
4. 2*y - a = 30
5. f + 3*z = 30

Let's solve this step by step:

First, we can solve equation 3 for z:

3. 6*z = 30 Divide both sides by 6: z = 5

Now, we can substitute the value of z into equations 2 and 5:

2. 2*5 + y = 30 10 + y = 30 y = 30 - 10 y = 20

3. f + 3*5 = 30 f + 15 = 30 f = 30 - 15 f = 15

Now, we have found the values of z, y, and f. Let's substitute these values into equations 1 and 4 to find the value of a:

1. X - 2a = 30 X - 2a = 30 X = 30 + 2*a

2. 2y - a = 30 220 - a = 30 40 - a = 30 -a = 30 - 40 -a = -10 a = 10

Now we have found the values of all the variables:

a = 10 y = 20 z = 5 f = 15

And X can be expressed in terms of a:

X = 30 + 2a X = 30 + 210 X = 30 + 20 X = 50

So, the solutions to the system of equations are: a = 10 y = 20 z = 5 f = 15 X = 50