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Solve the system by substitution. {:[8x-3y=-16],[7x+1=y]:} (◻,◻)

Solve the system by substitution.\newline8x−3y=−167x+1=y \begin{aligned} 8 x-3 y & =-16 \\ 7 x+1 & =y \end{aligned} \newline(□,□) (\square, \square)

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Q. Solve the system by substitution.\newline8x−3y=−167x+1=y \begin{aligned} 8 x-3 y & =-16 \\ 7 x+1 & =y \end{aligned} \newline(□,□) (\square, \square)
  1. Substitute Equations: Substitute the second equation into the first equation.\newlineThe second equation is given as 7x+1=y7x + 1 = y. We can use this to substitute for yy in the first equation, 8x−3y=−168x - 3y = -16.
  2. Use Substitution: Substitute yy with 7x+17x + 1 in the first equation.8x−3(7x+1)=−168x - 3(7x + 1) = -16
  3. Distribute and Combine: Distribute −3-3 across the terms in the parentheses.8x−21x−3=−168x - 21x - 3 = -16
  4. Isolate xx Term: Combine like terms.−13x−3=−16-13x - 3 = -16
  5. Solve for x: Add 33 to both sides of the equation to isolate the term with xx.\newline−13x=−16+3-13x = -16 + 3\newline−13x=−13-13x = -13
  6. Substitute xx for yy: Divide both sides by −13-13 to solve for xx.
    x=(−13)/(−13)x = (-13) / (-13)
    x=1x = 1
  7. Calculate yy Value: Substitute xx back into the second equation to solve for yy.\newline7x+1=y7x + 1 = y\newline7(1)+1=y7(1) + 1 = y
  8. Calculate y Value: Substitute xx back into the second equation to solve for yy. \newline7x+1=y7x + 1 = y\newline7(1)+1=y7(1) + 1 = y Calculate the value of yy.\newline7+1=y7 + 1 = y\newliney=8y = 8

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