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Y=2xY=2x 3x+y=203x +y =20

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Q. Y=2xY=2x 3x+y=203x +y =20
  1. Identify Equations: Identify the given system of equations.\newlineWe have two equations:\newline11) Y=2xY = 2x\newline22) 3x+Y=203x + Y = 20\newlineWe need to find the values of xx and yy that satisfy both equations simultaneously.
  2. Substitute YY in Second: Substitute the expression for YY from the first equation into the second equation.\newlineSince Y=2xY = 2x, we can replace YY in the second equation with 2x2x to get:\newline3x+2x=203x + 2x = 20
  3. Combine Like Terms: Combine like terms in the equation from Step 22.\newline3x+2x=5x3x + 2x = 5x\newlineSo the equation becomes:\newline5x=205x = 20
  4. Solve for x: Solve for x.\newlineTo find the value of x, we divide both sides of the equation by 55:\newline5x5=205\frac{5x}{5} = \frac{20}{5}\newlinex=4x = 4
  5. Substitute xx for YY: Substitute the value of xx back into the first equation to find yy. We know that Y=2xY = 2x, so: Y=2(4)Y = 2(4) Y=8Y = 8
  6. Check Solution: Check the solution in both original equations.\newlineFirst equation: Y=2xY = 2x\newline8=2(4)8 = 2(4)\newline8=88 = 8 (True)\newlineSecond equation: 3x+Y=203x + Y = 20\newline3(4)+8=203(4) + 8 = 20\newline12+8=2012 + 8 = 20\newline20=2020 = 20 (True)\newlineBoth equations are true, so the solution is correct.