Given the following System of equations:
[tex]\mleft\{\begin{aligned}y=4x-3 \\ y=-5x+9\end{aligned}\mright.[/tex]
You can find the exact solution as following:
1. You can make both equation equal to each other:
[tex]4x-3=-5x+9[/tex]
2. Now you must solve for the variable "x" in order to find its value. This is:
[tex]\begin{gathered} 4x+5x=9+3 \\ 9x=12 \\ x=\frac{12}{9} \\ \\ x=\frac{4}{3} \\ x=1.33 \end{gathered}[/tex]
3. Substitute the value of "x" into any original equation and evaluate, in order to find the value of "y":
[tex]\begin{gathered} y=4x-3 \\ y=4(1.33)-3 \\ y=2.32 \end{gathered}[/tex]
Then you get this solution written as an ordered pair:
[tex](1.33,2.32)[/tex]
You can determine that the best approximation of the exact solution is: Option A.
