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Solve the system by substitution. {:[-3x+3y=-12],[y=5x-8]:}

Solve the system by substitution.\newline−3x+3y=−12y=5x−8 \begin{aligned} -3 x+3 y & =-12 \\ y & =5 x-8 \end{aligned}

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Q. Solve the system by substitution.\newline−3x+3y=−12y=5x−8 \begin{aligned} -3 x+3 y & =-12 \\ y & =5 x-8 \end{aligned}
  1. Substitute yy with 5x−85x - 8: Substitute yy with 5x−85x - 8 in the first equation.\newline−3x+3y=−12-3x + 3y = -12 becomes −3x+3(5x−8)=−12-3x + 3(5x - 8) = -12.
  2. Distribute 33 to terms: Distribute 33 to the terms inside the parentheses.\newline−3x+3(5x)−3(8)=−12-3x + 3(5x) - 3(8) = -12\newline−3x+15x−24=−12-3x + 15x - 24 = -12
  3. Combine like terms: Combine like terms. 12x−24=−1212x - 24 = -12
  4. Add 2424 to isolate: Add 2424 to both sides of the equation to isolate the term with xx.12x−24+24=−12+2412x - 24 + 24 = -12 + 2412x=1212x = 12
  5. Divide both sides: Divide both sides by 1212 to solve for xx.\newline12x12=1212\frac{12x}{12} = \frac{12}{12}\newlinex=1x = 1
  6. Substitute x=1x = 1: Substitute x=1x = 1 into y=5x−8y = 5x - 8 to solve for yy.
    y=5(1)−8y = 5(1) - 8
    y=5−8y = 5 - 8
    y=−3y = -3

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