Stuck on solving for unknowns in part F and G help please?

a) the upper loop
1 18I12+ 13I18=30

(b) the lower loop
2 =5.00I36 - 18I12= 24

(c) the node on the left side
3 I12+I36=I18

(d) Solve the node equation for I36.
4 I12 - I18 =I36

e) Using the equation found in (d), eliminate I36 from the equation found in part (b).
5 5(I18-I12)-18I12=24

(f) Solve the equations found in part (a) and part (e) simultaneously for the two unknowns for I12 and I18, respectively.
I12 =......A
I18 =.......... A

(g) Substitute the answers found in part (f) into the node equation found in part (d), solving for I36.
I36 = .......A

Stuck on solving for unknowns in part F and G help please?

a) the upper loop
1 18I12+ 13I18=30

(b) the lower loop
2 =5.00I36 - 18I12= 24

(c) the node on the left side
3 I12+I36=I18

(d) Solve the node equation for I36.
4 I12 - I18 =I36

e) Using the equation found in (d), eliminate I36 from the equation found in part (b).
5 5(I18-I12)-18I12=24

(f) Solve the equations found in part (a) and part (e) simultaneously for the two unknowns for I12 and I18, respectively.
I12 =......A
I18 =.......... A

(g) Substitute the answers found in part (f) into the node equation found in part (d), solving for I36.
I36 = .......A

Hey man .. there is the answer

For neatness, let x = I₁₂ and y = I₁₈. So the equations are:
5y - 23x = 24 (equation 1)
18x+ 13y = 30 (equation 2)

Multiply equation 1 by 18/23 so the coefficients of x will be the same in both equations:
5(18/23)y - 23(18/23)x = 24(18/23)
3.913y - 18x = 18.783 (equation 3)

Now add left sides and right sides of equations 2 and 3:
3.913y - 18x + 18x+ 13y = 18.783 + 30
3.913y + 13y = 48.783
16.913y = 48.783
y = 48.783/16.913
. .= 2.884

So I₁₈ (=y) = 2.88A to 3 significant figures.

The rest should be straightforward.
^__^

To solve for the unknowns in part F and G, we need to follow these steps:

Step 1: Solve equation (a) and equation (e) simultaneously to find the values of I12 and I18.

Equation (a): 18I12 + 13I18 = 30
Equation (e): 5(I18 - I12) - 18I12 = 24

To solve this system of equations, we can use the method of substitution or elimination.

Let's solve it using substitution:
From equation (e), we can rearrange it to express I18 in terms of I12:
5(I18 - I12) - 18I12 = 24
5I18 - 5I12 - 18I12 = 24
5I18 - 23I12 = 24
5I18 = 23I12 + 24
I18 = (23I12 + 24)/5

Now, substitute this value of I18 into equation (a):
18I12 + 13((23I12 + 24)/5) = 30

Simplify the equation and solve for I12:
18I12 + (299I12 + 312)/5 = 30
90I12 + 299I12 + 312 = 150
389I12 = 150 - 312
389I12 = -162
I12 = -162/389

Now, substitute this value of I12 into the expression for I18 (from equation e) to find I18:
I18 = (23I12 + 24)/5

Substitute the value of I12:
I18 = (23(-162/389) + 24)/5

Now solve this equation to find the value of I18.

Step 2: Substitute the values of I12 and I18 into the node equation (d) to solve for I36.

Equation (d): I12 - I18 = I36

Substitute the values of I12 and I18 that we found into equation (d) and solve for I36.

I36 = ....

By following these steps, you should be able to solve for the unknowns in part F and G.