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Solve the system by substitution. {:[-x-6y=8],[-10 y=x]:} (◻,◻)

Solve the system by substitution.\newline−x−6y=8−10y=x \begin{array}{r} -x-6 y=8 \\ -10 y=x \end{array} \newline(□,□) (\square, \square)

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Q. Solve the system by substitution.\newline−x−6y=8−10y=x \begin{array}{r} -x-6 y=8 \\ -10 y=x \end{array} \newline(□,□) (\square, \square)
  1. Isolate xx: Isolate xx in the second equation.\newlineThe second equation is given as −10y=x-10y = x. We can rewrite this as x=−10yx = -10y to isolate xx.
  2. Substitute xx: Substitute xx in the first equation.\newlineThe first equation is −x−6y=8-x - 6y = 8. We substitute xx with −10y-10y from the second equation to get: −(−10y)−6y=8-(-10y) - 6y = 8.
  3. Simplify the equation: Simplify the equation.\newlineSimplifying the equation gives us 10y−6y=810y - 6y = 8, which simplifies further to 4y=84y = 8.
  4. Solve for y: Solve for y.\newlineDivide both sides of the equation by 44 to get y=8/4y = 8 / 4, which simplifies to y=2y = 2.
  5. Substitute yy back: Substitute yy back into the equation x=−10yx = -10y. Now that we know y=2y = 2, we substitute it back into the equation x=−10yx = -10y to find xx. This gives us x=−10(2)x = -10(2), which simplifies to x=−20x = -20.
  6. Write the solution: Write the solution as an ordered pair.\newlineThe solution to the system of equations is x=−20x = -20 and y=2y = 2. Therefore, the ordered pair is (−20,2)(-20, 2).

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