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{:[y=2x],[3x+y=20]:} The given system of equations has solution (x,y). What is the value of x ? Choose 1 answer: (A) 4 (B) 5 (c) 8 (D) 20

yamp;=2x3x+yamp;=20 \begin{aligned} y & =2 x \\ 3 x+y & =20 \end{aligned} \newlineThe given system of equations has solution (x,y) (x, y) . What is the value of x x ?\newlineChoose 11 answer:\newline(A) 44\newline(B) 55\newline(C) 88\newline(D) 2020

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Full solution

Q. y=2x3x+y=20 \begin{aligned} y & =2 x \\ 3 x+y & =20 \end{aligned} \newlineThe given system of equations has solution (x,y) (x, y) . What is the value of x x ?\newlineChoose 11 answer:\newline(A) 44\newline(B) 55\newline(C) 88\newline(D) 2020
  1. Write Equations: Write down the given system of equations.\newlineWe have the system of equations:\newline11) y=2xy = 2x\newline22) 3x+y=203x + y = 20
  2. Substitute and Simplify: Substitute the expression for yy from the first equation into the second equation.\newlineFrom equation 11) we have y=2xy = 2x. We can substitute this into equation 22) to get:\newline3x+2x=203x + 2x = 20
  3. Solve for x: Combine like terms and solve for x.\newline3x+2x=203x + 2x = 20\newline5x=205x = 20\newlineNow, divide both sides by 55 to solve for x:\newlinex=205x = \frac{20}{5}\newlinex=4x = 4
  4. Check Solution: Check the solution by substituting xx back into the original equations.\newlineSubstitute x=4x = 4 into the first equation:\newliney=2xy = 2x\newliney=2(4)y = 2(4)\newliney=8y = 8\newlineNow substitute x=4x = 4 and y=8y = 8 into the second equation:\newline3x+y=203x + y = 20\newline3(4)+8=203(4) + 8 = 20\newline12+8=2012 + 8 = 20\newlinex=4x = 400\newlineThe left side equals the right side, so the solution x=4x = 4 is correct.

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