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Solve the system by substitution. {:[-2x+5=y],[10 x-4y=-38]:} (◻,◻)

Solve the system by substitution.\newline−2x+5=y10x−4y=−38 \begin{aligned} -2 x+5 & =y \\ 10 x-4 y & =-38 \end{aligned} \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−2x+5=y10x−4y=−38 \begin{aligned} -2 x+5 & =y \\ 10 x-4 y & =-38 \end{aligned} \newline(□,□) (\square, \square)
  1. Isolate y: Isolate yy in the first equation.\newlineThe first equation is −2x+5=y-2x + 5 = y. We can rewrite this as y=−2x+5y = -2x + 5.
  2. Substitute expression for y: Substitute the expression for y into the second equation.\newlineThe second equation is 10x−4y=−3810x - 4y = -38. We substitute yy with −2x+5-2x + 5 to get 10x−4(−2x+5)=−3810x - 4(-2x + 5) = -38.
  3. Simplify and solve for x: Simplify and solve for x.\newline10x+8x−20=−3810x + 8x - 20 = -38\newline18x−20=−3818x - 20 = -38\newline18x=−38+2018x = -38 + 20\newline18x=−1818x = -18\newlinex=−1818x = \frac{-18}{18}\newlinex=−1x = -1
  4. Substitute xx back: Substitute xx back into the first equation to solve for yy. We have y=−2(−1)+5y = -2(-1) + 5. y=2+5y = 2 + 5 y=7y = 7
  5. Write solution as ordered pair: Write the solution as an ordered pair (x,y)(x, y). The solution is (−1,7)(-1, 7).

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