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Solve the system by substitution. {:[-6x+2=y],[5x+9y=-31]:} (◻,◻)

Solve the system by substitution.\newline−6x+2=y5x+9y=−31 \begin{array}{l} -6 x+2=y \\ 5 x+9 y=-31 \end{array} \newline(□,□) (\square, \square)

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Q. Solve the system by substitution.\newline−6x+2=y5x+9y=−31 \begin{array}{l} -6 x+2=y \\ 5 x+9 y=-31 \end{array} \newline(□,□) (\square, \square)
  1. Solve for yy: Solve the first equation for yy in terms of xx.−6x+2=y-6x + 2 = yThis gives us yy directly in terms of xx, so we can substitute this expression for yy into the second equation.
  2. Substitute into second equation: Substitute y=−6x+2y = -6x + 2 into the second equation.\newline5x+9(−6x+2)=−315x + 9(-6x + 2) = -31\newlineNow we will distribute the 99 and combine like terms.
  3. Distribute and combine terms: Distribute and combine like terms.\newline5x−54x+18=−315x - 54x + 18 = -31\newline−49x+18=−31-49x + 18 = -31\newlineNow we will solve for xx by isolating the variable.
  4. Isolate variable xx: Solve for xx.
    −49x+18=−31-49x + 18 = -31
    Subtract 1818 from both sides.
    −49x=−31−18-49x = -31 - 18
    −49x=−49-49x = -49
    Divide both sides by −49-49.
    x=(−49)/(−49)x = (-49) / (-49)
    x=1x = 1
    We have found the value of xx.
  5. Solve for xx: Substitute x=1x = 1 into y=−6x+2y = -6x + 2 to find yy.y=−6(1)+2y = -6(1) + 2y=−6+2y = -6 + 2y=−4y = -4We have found the value of yy.

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