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Solve the system by substitution. {:[3y-8=x],[7x+10 y=37]:} (◻,◻)

Solve the system by substitution.\newline3y−8=x7x+10y=37 \begin{aligned} 3 y-8 & =x \\ 7 x+10 y & =37 \end{aligned} \newline(□,□) (\square, \square)

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Q. Solve the system by substitution.\newline3y−8=x7x+10y=37 \begin{aligned} 3 y-8 & =x \\ 7 x+10 y & =37 \end{aligned} \newline(□,□) (\square, \square)
  1. Identify Equation for Substitution: Identify the first equation to use for substitution.\newlineThe first equation is 3y−8=x3y - 8 = x. We can use this equation to express xx in terms of yy, which will allow us to substitute this expression into the second equation.
  2. Substitute Expression into Second Equation: Substitute the expression for xx from the first equation into the second equation.\newlineThe second equation is 7x+10y=377x + 10y = 37. Substituting xx with 3y−83y - 8 gives us:\newline7(3y−8)+10y=377(3y - 8) + 10y = 37
  3. Distribute and Combine Like Terms: Distribute and combine like terms.\newline21y−56+10y=3721y - 56 + 10y = 37\newline31y−56=3731y - 56 = 37
  4. Solve for y: Solve for y.\newlineAdd 5656 to both sides of the equation:\newline31y−56+56=37+5631y - 56 + 56 = 37 + 56\newline31y=9331y = 93\newlineNow, divide both sides by 3131:\newliney=9331y = \frac{93}{31}\newliney=3y = 3
  5. Substitute Value Back for x: Substitute the value of yy back into the first equation to solve for xx. Using the first equation 3y−8=x3y - 8 = x, substitute yy with 33: x=3(3)−8x = 3(3) - 8 x=9−8x = 9 - 8 x=1x = 1
  6. Write Solution as Ordered Pair: Write the solution as an ordered pair (x,y)(x, y). The solution is (1,3)(1, 3).

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