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{:[2y-x=0],[x=y+7]:} If (x,y) satisfies the given system of equations, what is the value of x ?

2y−x=0 2 y-x=0 \newlinex=y+7 x=y+7 \newlineIf (x,y) (x, y) satisfies the given system of equations, what is the value of x x ?

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Full solution

Q. 2y−x=0 2 y-x=0 \newlinex=y+7 x=y+7 \newlineIf (x,y) (x, y) satisfies the given system of equations, what is the value of x x ?
  1. Solve first equation for y: We have the system of equations:\newline{:\begin{cases}2y-x=0\x=y+7\end{cases}:}\newlineLet's solve the first equation for y.\newline2y−x=02y - x = 0\newlineAdd xx to both sides to isolate yy terms.\newline2y=x2y = x\newlineDivide both sides by 22 to solve for yy.\newliney=x2y = \frac{x}{2}
  2. Substitute yy into second equation: Now let's substitute y=x2y = \frac{x}{2} into the second equation.\newlinex=y+7x = y + 7\newlineReplace yy with x2\frac{x}{2}.\newlinex=(x2)+7x = \left(\frac{x}{2}\right) + 7\newlineMultiply both sides by 22 to clear the fraction.\newline2x=x+142x = x + 14
  3. Solve for x: Now, let's solve for xx. Subtract xx from both sides. 2x−x=142x - x = 14 x=14x = 14

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