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Solve the system by substitution. {:[-2y+10=x],[-x-3y=-8]:} (◻,◻)

Solve the system by substitution.\newline−2y+10=x−x−3y=−8 \begin{array}{l} -2 y+10=x \\ -x-3 y=-8 \end{array} \newline(□,□) (\square, \square)

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Solve a system of equations in three variables using substitutionright chevron icon

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Q. Solve the system by substitution.\newline−2y+10=x−x−3y=−8 \begin{array}{l} -2 y+10=x \\ -x-3 y=-8 \end{array} \newline(□,□) (\square, \square)
  1. Isolate x: Isolate xx in the first equation.\newlineThe first equation is −2y+10=x-2y + 10 = x. We can rewrite this as x=−2y+10x = -2y + 10.
  2. Substitute xx: Substitute the expression for xx into the second equation.\newlineThe second equation is −x−3y=−8-x - 3y = -8. Substituting xx from the first equation, we get −(−2y+10)−3y=−8-( -2y + 10) - 3y = -8.
  3. Simplify and solve: Simplify the equation and solve for yy.2y−10−3y=−82y - 10 - 3y = -8−y−10=−8-y - 10 = -8Add 1010 to both sides:−y=2-y = 2Multiply both sides by −1-1:y=−2y = -2
  4. Substitute yy into xx: Substitute the value of yy back into the first equation to find xx. Using the first equation x=−2y+10x = -2y + 10 and substituting y=−2y = -2, we get: x=−2(−2)+10x = -2(-2) + 10 x=4+10x = 4 + 10 x=14x = 14

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