We have to write the system of equations and find the solution.
Our variables are the miles of each car in one week, so we call x for car 1 and y for car 2 the miles that each car drove.
One equation is that the two cars drove a combined total of 975 miles, so:
[tex]x+y=975[/tex]And the other equation, is that ths sum of their fuel efficiences are 35 miles per gallon. Also, we know that car 1 consumed 25 gallons in one week and car 2 consumed 30 gallons on one week, so:
[tex]\frac{x}{25}+\frac{y}{30}=35[/tex]To find the solution we can isolate x from the first equation and replace into the second equation:
[tex]\begin{gathered} x+y=975 \\ x=975-y \end{gathered}[/tex]Replacing into second equation and isolate y:
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