$$ \left.\begin{array}{l} ext { Solve the system of equations shown below by hand calculation } \ \qquad \begin{array}{l}5 x-y=0 \ 3 x+5 y=56\end{array} \ (x, y)=(\square\end{array} ight) $$

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$$ \left.\begin{array}{l}	ext { Solve the system of equations shown below by hand calculation } \ \qquad \begin{array}{l}5 x-y=0 \ 3 x+5 y=56\end{array} \ (x, y)=(\square\end{array}ight) $$

UpStudy AI · Accepted Answer

Solve the system of equations $$ 5x-y=0;3x+5y=56 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}5x-y=0\3x+5y=56\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}y=5x\3x+5y=56\end{array}ight.$$
- step2: Substitute the value of $$y:$$
  $$3x+5	imes 5x=56$$
- step3: Simplify:
  $$28x=56$$
- step4: Divide both sides:
  $$\frac{28x}{28}=\frac{56}{28}$$
- step5: Divide the numbers:
  $$x=2$$
- step6: Substitute the value of $$x:$$
  $$y=5	imes 2$$
- step7: Calculate:
  $$y=10$$
- step8: Calculate:
  $$\left\{ \begin{array}{l}x=2\y=10\end{array}ight.$$
- step9: Check the solution:
  $$\left\{ \begin{array}{l}x=2\y=10\end{array}ight.$$
- step10: Rewrite:
  $$\left(x,yight) = \left(2,10ight)$$
The solution to the system of equations is $$ (x, y) = (2, 10) $$.
$$ (x, y) = (2, 10) $$

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