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Solve the system by substitution. {:[-2x-2y=-32],[-9y=x]:}

Solve the system by substitution.\newline−2x−2y=−32−9y=x \begin{aligned} -2 x-2 y & =-32 \\ -9 y & =x \end{aligned}

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Q. Solve the system by substitution.\newline−2x−2y=−32−9y=x \begin{aligned} -2 x-2 y & =-32 \\ -9 y & =x \end{aligned}
  1. Identify Equation for Substitution: Identify the easier equation to use for substitution.\newlineThe second equation, −9y=x-9y = x, is already solved for xx, making it the easiest to use for substitution.
  2. Substitute xx into First Equation: Substitute xx from the second equation into the first equation.\newlineThe first equation is −2x−2y=−32-2x - 2y = -32. Substituting xx with −9y-9y from the second equation gives us −2(−9y)−2y=−32-2(-9y) - 2y = -32.
  3. Simplify and Solve for yy: Simplify the equation and solve for yy.
    18y−2y=−3218y - 2y = -32
    16y=−3216y = -32
    Divide both sides by 1616 to find yy.
    y=−32/16y = -32 / 16
    y=−2y = -2
  4. Substitute yy into Second Equation: Substitute yy back into the second equation to find xx. The second equation is −9y=x-9y = x. Substituting yy with −2-2 gives us −9(−2)=x-9(-2) = x. x=18x = 18
  5. Write Solution as Ordered Pair: Write the solution as an ordered pair (x,y)(x, y). The solution is (18,−2)(18, -2).

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