Greetings!
Substitute:
[tex]x+y=1000 \\ x=1000-y[/tex]
Now we can input this into the other equation so, we only have one variable.
Solve for y.
[tex]0.05(1000-y)+0.06y=57[/tex]
Distribute the parenthesis.
[tex]50-0.05y+0.06y=57[/tex]
Combine Like Terms.
[tex]50-0.01y=57[/tex]
Add -50 to both sides.
[tex](50-0.01y)+(-50)=(57)+(-50)[/tex]
Simplify.
[tex]0.01y=7[/tex]
Divide both sides by 0.01.
[tex](0.01y)/0.01=(7)/0.01[/tex]
Simplify.
[tex]y=700[/tex]
Input this value into the other equation.
[tex]x+700=1000[/tex]
Add -700 to both sides.
[tex](x+700)+(-700)=(1000)+(-700)[/tex]
Simplify.
[tex]x=300[/tex]
The answer would be 300,700
Hope this helps.
-Benjamin
