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Find the solution of the system of equations. {:[2x+3y=19],[2x-6y=-44](_________,________)":}

Find the solution of the system of equations.\newline2x+3y=192x−6y=−44 \begin{array}{l} 2 x+3 y=19 \\ 2 x-6 y=-44 \end{array} \newline(_________,________)

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Q. Find the solution of the system of equations.\newline2x+3y=192x−6y=−44 \begin{array}{l} 2 x+3 y=19 \\ 2 x-6 y=-44 \end{array} \newline(_________,________)
  1. Label Equations: First, let's label the equations for reference:\newlineEquation 11: 2x+3y=192x + 3y = 19\newlineEquation 22: 2x−6y=−442x - 6y = -44
  2. Subtract Equations: Subtract Equation 22 from Equation 11 to eliminate xx:(2x+3y)−(2x−6y)=19−(−44)(2x + 3y) - (2x - 6y) = 19 - (-44)
  3. Perform Subtraction: Perform the subtraction: 2x−2x+3y+6y=19+442x - 2x + 3y + 6y = 19 + 44
  4. Simplify Equation: Simplify the equation: 9y=639y = 63
  5. Divide for yy: Divide both sides by 99 to solve for yy:y=639y = \frac{63}{9}
  6. Calculate y: Calculate the value of y:\newliney=7y = 7
  7. Substitute for x: Now substitute y=7y = 7 into Equation 11 to solve for x:\newline2x+3(7)=192x + 3(7) = 19
  8. Perform Multiplication: Perform the multiplication: 2x+21=192x + 21 = 19
  9. Subtract to Solve xx: Subtract 2121 from both sides to solve for xx:2x=19−212x = 19 - 21
  10. Divide for xx: Calculate the value of xx:2x=−22x = -2
  11. Calculate xx: Divide both sides by 22 to solve for xx:x=−22x = \frac{-2}{2}
  12. Final x Value: Calculate the final value of x:\newlinex=−1x = -1

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