Answer :
The price of the adult ticket to a basketball game is $20.
System of Linear Equations
System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
- STEP 1 - Convert the text of problem in system of equations
2a+3n=67
3a+2n=78
where: a= adultos and n =niños
- STEP 2 - Find the variables a and n.
[tex]\begin{bmatrix}2a+3n=67\;\; equation1\\\ 3a+2n=78\;\; equation2\end{bmatrix}\\ \\ \\ \begin{bmatrix}2a+3n=67\; *(-3)\\ 3a+2n=78\; *(2)\end{bmatrix}\\ \\ \\ \begin{bmatrix}-6a-9n=-201\\ 6a+4n=156\end{bmatrix}\\ \\ \\ Sum\; of\; equations\\ \\ -6a-9n+6a+4n=-201+156\\ -9n+4n=-201+156\\ -5n=-45\\ n=\frac{-45}{-5} =9\\\\\\ Replacing\; n\; in\; equation 1\\\\2a+3*9=67\\ 2a+27=67\\ 2a=67-27\\ 2a=40\\ a=20[/tex]
Thus, a=20 and n=9.
Learn more about the system of equations here:
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