Solving simultaneous equations with R

Question

Suppose I have the following equations:

 x + 2y + 3z = 20  
2x + 5y + 9z = 100  
5x + 7y + 8z = 200

How do I solve these equations for

Answer 1

Another approach is to model the equations using lm as follows:

lm(b ~ . + 0, 
   data = data.frame(x = c(1, 2, 5), 
                     y = c(2, 5, 7), 
                     z = c(3, 9, 8), 
                     b = c(20, 100, 200)))

which produces

Coefficients:
   x     y     z  
 320  -360   140

If you use the tibble package you can even make it read just like the original equations:

lm(b ~ . + 0, 
   tibble::tribble(
     ~x, ~y, ~z,  ~b,
      1,  2,  3,  20,
      2,  5,  9, 100,
      5,  7,  8, 200))

which produces the same output.