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

Question

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

Answer 1

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

Answer 2

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.
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