Solve it! TT \( \sqrt{ \pm} \) Here is the system we created on the last slide.... Solve it! \[ \begin{array}{l} 30 x+4 y=1,040 \\ 12 x+16 y=2,000 \end{array} \] Write your answer as an ordered pair ( \( x, y \) ) Explain the meaning of your solution using a sentence or two. \( \sqrt{ \pm} \) Submit

Solve the system of equations \( 30x+4y=1040;12x+16y=2000 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}30x+4y=1040\\12x+16y=2000\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{520-2y}{15}\\12x+16y=2000\end{array}\right.\) - step2: Substitute the value of \(x:\) \(12\times \frac{520-2y}{15}+16y=2000\) - step3: Multiply the terms: \(\frac{4\left(520-2y\right)}{5}+16y=2000\) - step4: Multiply both sides of the equation by LCD: \(\left(\frac{4\left(520-2y\right)}{5}+16y\right)\times 5=2000\times 5\) - step5: Simplify the equation: \(2080+72y=10000\) - step6: Move the constant to the right side: \(72y=10000-2080\) - step7: Subtract the numbers: \(72y=7920\) - step8: Divide both sides: \(\frac{72y}{72}=\frac{7920}{72}\) - step9: Divide the numbers: \(y=110\) - step10: Substitute the value of \(y:\) \(x=\frac{520-2\times 110}{15}\) - step11: Calculate: \(x=20\) - step12: Calculate: \(\left\{ \begin{array}{l}x=20\\y=110\end{array}\right.\) - step13: Check the solution: \(\left\{ \begin{array}{l}x=20\\y=110\end{array}\right.\) - step14: Rewrite: \(\left(x,y\right) = \left(20,110\right)\) The solution to the system of equations is \( (x, y) = (20, 110) \). This means that when \( x = 20 \) and \( y = 110 \), both equations are satisfied. In other words, the point (20, 110) is a solution to the system of equations.