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Solve the system by substitution. {:[8x+8y=-40],[x=4y+5]:} (◻,◻)

Solve the system by substitution.\newline8x+8y=−40x=4y+5 \begin{aligned} 8 x+8 y & =-40 \\ x & =4 y+5 \end{aligned} \newline(□,□) (\square, \square)

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Q. Solve the system by substitution.\newline8x+8y=−40x=4y+5 \begin{aligned} 8 x+8 y & =-40 \\ x & =4 y+5 \end{aligned} \newline(□,□) (\square, \square)
  1. Substitute xx in first equation: Substitute the expression for xx from the second equation into the first equation.\newlineGiven the second equation x=4y+5x = 4y + 5, we can substitute xx in the first equation 8x+8y=−408x + 8y = -40.\newline8(4y+5)+8y=−408(4y + 5) + 8y = -40
  2. Distribute and combine like terms: Distribute 88 to the terms inside the parentheses and combine like terms.\newline8×4y+8×5+8y=−408 \times 4y + 8 \times 5 + 8y = -40\newline32y+40+8y=−4032y + 40 + 8y = -40\newline40y+40=−4040y + 40 = -40
  3. Isolate y term: Subtract 4040 from both sides of the equation to isolate the term with yy.\newline40y+40−40=−40−4040y + 40 - 40 = -40 - 40\newline40y=−8040y = -80
  4. Solve for y: Divide both sides of the equation by 4040 to solve for y.\newline40y40=−8040\frac{40y}{40} = \frac{-80}{40}\newliney=−2y = -2
  5. Substitute yy back for xx: Substitute the value of yy back into the second equation to solve for xx.
    x=4y+5x = 4y + 5
    x=4(−2)+5x = 4(-2) + 5
    x=−8+5x = -8 + 5
    x=−3x = -3
  6. Write solution as ordered pair: Write the solution as an ordered pair (x,y)(x, y).\newlineThe solution is (−3,−2)(-3, -2).

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