Question 90518
You are being asked to find the amounts invested at each rate.  
Let x = the amount invested at 4% and y = the amount invested at 2.25%.
Since the total money invested was $33,000, your first equation is x + y =$33,000.  Since the total interest is $970, your second equation is 4%x+2.25%y = $970.

Solve the system 
   {{{x+y = 33000}}}
{{{.04x+.0225y = 970}}}   

Solve the first equation for x.  Substitute in the second equation and solve for y.
{{{x + y = 33000}}}
{{{x = 33000 - y}}} 
Then
{{{.04(33000-y) + .0225y = 970}}}
{{{1320 - .04y + .0225y = 970 }}}
{{{-.0175y + 1320 - 1320 = 970-1320}}}
{{{-.0175y = - 350}}}
{{{y =  20000}}}
Now you can solve for x
{{{x + 20000 = 33000}}}
{{{x = 13000}}}
So, your answer is $13,000 invested at 4% and $20000 invested at %2.25.
You can check the second equation.
{{{.04x+.0225y = 970}}}   
{{{.04(13000)+.0225(20000) = 970}}}
{{{520 + 450 =970}}}
{{{970 = 970 }}} checks!

Good Luck!