Let x = price of taco
Let y = price of glass of milk
"The cost of a breakfast taco and a small glass of milk is $5.10" translates to
[tex]x+y=5.10[/tex]"The cost for two tacos and three small glasses of milk is $11.80" translates to
[tex]2x+3y=11.80[/tex]We now have the system
[tex]\begin{gathered} x+y=5.10\text{ (first equation)} \\ 2x+3y=11.80\text{ (second equation)} \end{gathered}[/tex]Solve for y using the first equation
[tex]\begin{gathered} x+y=5.10 \\ y=5.10-x\text{ (third equation)} \end{gathered}[/tex]Use the third equation and substitute it to the second equation
[tex]\begin{gathered} 2x+3y=11.80 \\ 2x+3(5.10-x)=11.80 \\ 2x+15.3-3x=11.80 \\ -x=11.80-15.3 \\ -x=-3.5 \\ x=3.5 \end{gathered}[/tex]Substitute the value of x to the third equation and we have
[tex]\begin{gathered} y=5.10-3.5 \\ y=1.6 \end{gathered}[/tex]Since x is the price of taco, the cost of a taco is $3.50.
