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Solve the system by substitution. {:[-3x-8=y],[-8x-7y=-48]:} (◻,◻)

Solve the system by substitution.\newline−3x−8=y−8x−7y=−48 \begin{aligned} -3 x-8 & =y \\ -8 x-7 y & =-48 \end{aligned} \newline(□,□) (\square, \square)

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Q. Solve the system by substitution.\newline−3x−8=y−8x−7y=−48 \begin{aligned} -3 x-8 & =y \\ -8 x-7 y & =-48 \end{aligned} \newline(□,□) (\square, \square)
  1. Identify equation for substitution: Identify the first equation to use for substitution.\newlineThe first equation is −3x−8=y-3x - 8 = y. We can use this to express yy in terms of xx.
  2. Substitute expression into second equation: Substitute the expression for yy from the first equation into the second equation.\newlineThe second equation is −8x−7y=−48-8x - 7y = -48. Substituting yy from the first equation, we get:\newline−8x−7(−3x−8)=−48-8x - 7(-3x - 8) = -48
  3. Simplify and solve for xx: Simplify and solve for xx.\newlineDistribute the −7-7 through the parentheses:\newline−8x+21x+56=−48-8x + 21x + 56 = -48\newlineCombine like terms:\newline13x+56=−4813x + 56 = -48\newlineSubtract 5656 from both sides:\newline13x=−48−5613x = -48 - 56\newline13x=−10413x = -104\newlineDivide both sides by 1313:\newlinex=−104/13x = -104 / 13\newlinexx00
  4. Substitute xx back to solve for yy: Substitute the value of xx back into the first equation to solve for yy. Substitute −8-8 for xx in −3x−8=y-3x - 8 = y: −3(−8)−8=y-3(-8) - 8 = y 24−8=y24 - 8 = y y=16y = 16

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