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Solve the system by substitution. {:[y=5x-10],[-4x+3y=36]:}

Solve the system by substitution.\newliney=5x−10−4x+3y=36 \begin{aligned} y & =5 x-10 \\ -4 x+3 y & =36 \end{aligned}

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Q. Solve the system by substitution.\newliney=5x−10−4x+3y=36 \begin{aligned} y & =5 x-10 \\ -4 x+3 y & =36 \end{aligned}
  1. Identify Equation: Identify the equation that can be easily substituted.\newlineIn this case, we have yy expressed in terms of xx in the first equation: y=5x−10y = 5x - 10.
  2. Substitute Expression: Substitute the expression for yy into the second equation.\newlineThe second equation is −4x+3y=36-4x + 3y = 36. We will replace yy with 5x−105x - 10.\newline−4x+3(5x−10)=36-4x + 3(5x - 10) = 36
  3. Distribute and Combine: Distribute and combine like terms.\newline−4x+15x−30=36-4x + 15x - 30 = 36\newline11x−30=3611x - 30 = 36
  4. Solve for x: Solve for x.\newlineAdd 3030 to both sides of the equation.\newline11x−30+30=36+3011x - 30 + 30 = 36 + 30\newline11x=6611x = 66\newlineDivide both sides by 1111.\newlinex=6611x = \frac{66}{11}\newlinex=6x = 6
  5. Substitute for y: Substitute the value of xx back into the first equation to solve for yy.\newliney=5x−10y = 5x - 10\newliney=5(6)−10y = 5(6) - 10\newliney=30−10y = 30 - 10\newline$y = \(20\)
  6. Write Ordered Pair: Write the solution as an ordered pair \((x, y)\). The solution is \((6, 20)\).

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