A medical lab technician needs to determine how much \( 16 \% \) hydrochloric acid (HCL of \( 10 \% \) solution. Use the system of equations in which x is the amount of \( 16 \% \) solut \( \begin{array}{l}x+y=39 \\ 16 x+7 y=390\end{array} \)

Solve the system of equations \( x+y=39;16x+7y=390 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x+y=39\\16x+7y=390\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=39-y\\16x+7y=390\end{array}\right.\) - step2: Substitute the value of \(x:\) \(16\left(39-y\right)+7y=390\) - step3: Simplify: \(624-9y=390\) - step4: Move the constant to the right side: \(-9y=390-624\) - step5: Subtract the numbers: \(-9y=-234\) - step6: Change the signs: \(9y=234\) - step7: Divide both sides: \(\frac{9y}{9}=\frac{234}{9}\) - step8: Divide the numbers: \(y=26\) - step9: Substitute the value of \(y:\) \(x=39-26\) - step10: Simplify: \(x=13\) - step11: Calculate: \(\left\{ \begin{array}{l}x=13\\y=26\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=13\\y=26\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(13,26\right)\) The solution to the system of equations is \( x = 13 \) and \( y = 26 \). This means that the medical lab technician needs to mix 13 units of 16% hydrochloric acid with 26 units of 10% hydrochloric acid to obtain a 39 unit solution.