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Solve the system by substitution. {:[3x-8y=9],[x=3y+6]:} (◻,◻)

Solve the system by substitution.\newline3x−8y=9x=3y+6 \begin{aligned} 3 x-8 y & =9 \\ x & =3 y+6 \end{aligned} \newline(□,□) (\square, \square)

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Q. Solve the system by substitution.\newline3x−8y=9x=3y+6 \begin{aligned} 3 x-8 y & =9 \\ x & =3 y+6 \end{aligned} \newline(□,□) (\square, \square)
  1. Identify Equation for Substitution: Identify the equation that can be used for substitution.\newlineWe are given the system of equations:\newline3x−8y=93x - 8y = 9\newlinex=3y+6x = 3y + 6\newlineThe second equation, x=3y+6x = 3y + 6, is already solved for xx, which makes it easy to substitute into the first equation.
  2. Substitute xx into First Equation: Substitute x=3y+6x = 3y + 6 into the first equation.\newlineSubstitute the expression for xx from the second equation into the first equation:\newline3(3y+6)−8y=93(3y + 6) - 8y = 9
  3. Distribute and Combine Terms: Distribute and combine like terms.\newline3(3y)+3(6)−8y=93(3y) + 3(6) - 8y = 9\newline9y+18−8y=99y + 18 - 8y = 9\newlineCombine like terms:\newline(9y−8y)+18=9(9y - 8y) + 18 = 9\newliney+18=9y + 18 = 9
  4. Solve for y: Solve for y.\newlineSubtract 1818 from both sides of the equation to isolate yy:\newliney+18−18=9−18y + 18 - 18 = 9 - 18\newliney=−9y = -9
  5. Substitute yy into Second Equation: Substitute y=−9y = -9 into the second equation to find xx.\newlineSubstitute y=−9y = -9 into x=3y+6x = 3y + 6:\newlinex=3(−9)+6x = 3(-9) + 6
  6. Calculate x Value: Calculate the value of x.\newlinex=−27+6x = -27 + 6\newlinex=−21x = -21
  7. Write Solution as Ordered Pair: Write the solution as an ordered pair (x,y)(x, y). The solution to the system of equations is (−21,−9)(-21, -9).

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