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Sagot :
Let x and y the time it takes Tanvi to do a push-up and a sit-up, respectively; thus, the system of equations is
[tex]\begin{cases}18x+11y=76 \\ 7x+19y=59\end{cases}[/tex]To solve it using elimination, multiply the second equation by 18/7 and subtract the result to the first equation, as shown below
[tex]\begin{gathered} \frac{18}{7}(7x+19y)=\frac{18}{7}\cdot59 \\ \Rightarrow18x+\frac{18}{7}\cdot19y=\frac{18}{7}\cdot59 \\ \Rightarrow18x+\frac{342}{7}y=\frac{1062}{7} \end{gathered}[/tex]Then,
[tex]\begin{gathered} 18x+11y-(18x+\frac{342}{7}y)=76-\frac{1062}{7} \\ \Rightarrow(11-\frac{342}{7})y=76-\frac{1062}{7} \\ \Rightarrow y=\frac{76-\frac{1062}{7}}{(11-\frac{342}{7})} \\ \Rightarrow y=2 \end{gathered}[/tex]Substitute the value of y=2 into the first equation,
[tex]\begin{gathered} y=2 \\ \Rightarrow18x+11y=18x+22 \\ \Rightarrow18x+22=76 \\ \Rightarrow18x=54 \\ \Rightarrow x=3 \end{gathered}[/tex]Thus, the answer is x=3, y=2. 3 seconds per push-up and 2 seconds per sit-up
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