91Ó°ÊÓ

We are given that Mark burn $510$calories for doing $40$minutes of Bikram hot yoga and $10$minutes of jumping jacks and for doing $30$minutes of Bikram hot yoga and $20$minutes of jumping jacks he burns$470$ calories.

Let $x$be the calories burn per minute for doing Bikram hot yoga and $y$be the calories burn per minute for doing jumping jacks.

The equations representing the calories burned are,

$$\begin{gathered} 40x+10y=510 \\ 30x+20y=470 \end{gathered}$$

Multiplying $2$in the first equation, we get

$$\begin{gathered} 2(40x+10y)=2×510 \\ 80x+20y=1020 \end{gathered}$$

Now, Subtracting the equations, we get

$50x=550$

Dividing by $50$, we get

$x=11$

Putting the value of $x$in second equation, we get

$$\begin{gathered} 30×11+20y=470 \\ 330+20y=470 \\ 20y=470-330 \\ 20y=140 \end{gathered}$$

Dividing by $20$, we get

$y=7$

Checking the solution by putting the value of $x,y$in the equations, we get

role="math" localid="1644599343600" $$\begin{gathered} 40x+10y=510 \\ 40\left(11\right)+10\left(7\right)=510 \\ 440+70=510 \\ 510=510 \\ 30x+20y=470 \\ 30\left(11\right)+20\left(7\right)=470 \\ 330+140=470 \\ 470=470 \end{gathered}$$

This is true, hence the solution is correct.