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]
