Question

1. Solve the system of equations 3r – 4s = 0 and 2r + 5s = 23.

Answer 1

3r-4s=0

2r+5s=23
2r=23-5s
r=(23-5s)/2

then 3(23-5s)/2=4s
69-15s=8s
69=23s
s=3
and r=(23-15)/2=4
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Answer 2

4s = 3r
s = 3/4*r
plug this into the second eqution and solve for the other variable:
2r +5(3/4)r = 23
23/4*r = 23
r = 4
plug this r into the above equation we solved:
s = 3/4*r
s = 3/4*4
s = 3
system is:
{r=4, s=3}