hi, i am doing a electronic engineering course and have come up with the simultaneous equations thati need to answer. any help on it? many thanks. liam
10x - 10 + 20y - 20 = 0
+20-20y+40(y-x)= 0
Hello,
In the first equation, divide by 10, then group :
$\displaystyle 10x-10+20y-20=0 \Longleftrightarrow x-1+2y-2=0 \Longleftrightarrow x-3+2y=0$
In the second equation, divide by 20, then develop :
$\displaystyle 20-20y+40(y-x)=0 \Longleftrightarrow 1-y+2(y-x)=0 \Longleftrightarrow 1+y-2x=0 \implies y=2x-1$
Therefore, by substituting in the first equation :
$\displaystyle x-3+2(2x-1)=0 \implies x-3+4x-2=0 \implies 5x-5=0 \implies \boxed{x=1}$
$\displaystyle y=2x-1=2(1)-1=\boxed{1}$
Simplifying your 2 equations, you get:
$\displaystyle 10x + 20y = 30$
$\displaystyle -40x + 20y = -20$
From here, I know 3 ways to solve. For the elimination method, go here:
2 Unknowns by Elimination Calculator
Enter those 2 equations and press the solve button.
I get (x,y) = (1,1) Plugging those back into the original equations, those work.
You could also use the substitution method here:
2 Unknowns by Substitution Calculator
or Cramer's method here:
2 Unknown Cramer's Method Calculator
Let me know if you have questions.