How can I solve the following problem using a set of two algebraic equations?Mr Stein invested a total of $100,000 in two companies for a year....

There are two ways to do this type of question. One way is
to use one varible and use the information given to solve for the
equation

The other type, which is what you wanted, uses two
varibles.

Let X be the number of dollars invested in
Company A and Y represent the number of dollars in Company
B

Since the total investment is 100,000 dollars, we have
the equation

1.               
X+Y=100,000

There is another piece of information given,
which is that the total return rate is 8%, so that we have another
equation

money gained in Company A + money gained in
Company B= total money earned

Money earned in Company A is
X*13%=0.13X

Money earned in Company B = Y * (-3%)=-0.03Y
(since it was a loss, there should be a negative sign)

the
total money earned is : 100,000*8%=800000/100=8000
dollars

the equation is

2.    
0.13 X-0.03y=8000

rewriting the first equation, we
have:

X=100,000 - Y

substitute
that answer into the second equation, we
have:

0.13(100,000-Y)-0.03Y=8000

13000-0.16Y=8000

0.16Y=5000

Y=31250

then
x = 100000-31250=68750