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{:[(1)/(3)x+3y=4],[2x-4=2y]:} Consider the given system of equations. If (x,y) is the solution to the system, then what is the value of x-y ?

13x+3y=4 \frac{1}{3} x+3 y=4 \newline2x−4=2y 2 x-4=2 y \newlineConsider the given system of equations. If (x,y) (x, y) is the solution to the system, then what is the value of x−y x-y ?

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Q. 13x+3y=4 \frac{1}{3} x+3 y=4 \newline2x−4=2y 2 x-4=2 y \newlineConsider the given system of equations. If (x,y) (x, y) is the solution to the system, then what is the value of x−y x-y ?
  1. Write Equations: Write down the given system of equations.\newlineThe system of equations is:\newline{13x+3y=42x−4=2y\begin{cases} \frac{1}{3}x + 3y = 4 \\ 2x - 4 = 2y \end{cases}
  2. Solve for y: Solve the second equation for y.\newline2x−4=2y2x - 4 = 2y\newlineDivide both sides by 22 to isolate y:\newliney=x−2y = x - 2
  3. Substitute y into first equation: Substitute the expression for y from Step 22 into the first equation.\newline13x+3(x−2)=4\frac{1}{3}x + 3(x - 2) = 4
  4. Combine terms in first equation: Distribute and combine like terms in the first equation.\newline13x+3x−6=4\frac{1}{3}x + 3x - 6 = 4\newlineCombine the x terms:\newline13x+93x=4+6\frac{1}{3}x + \frac{9}{3}x = 4 + 6\newline103x=10\frac{10}{3}x = 10
  5. Solve for x: Solve for x.\newlineMultiply both sides by 310\frac{3}{10} to isolate x:\newlinex=10⋅310x = 10 \cdot \frac{3}{10}\newlinex=3x = 3
  6. Substitute x into y expression: Substitute the value of x into the expression for y found in Step 22.\newliney=3−2y = 3 - 2\newliney=1y = 1
  7. Calculate x - y: Calculate the value of x - y.\newlinex−y=3−1x - y = 3 - 1\newlinex−y=2x - y = 2

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