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Estimate the solution to the system of equations. You can use the interactive graph below to find the solution. {[y=4x-2],[y=x+3]:} Choose 1 answer: (A) x=(2)/(3),y=4(2)/(3) (B) x=1(2)/(3),y=3(2)/(3) (C) x=(2)/(3),y=3(2)/(3) (D) x=1(2)/(3),y=4(2)/(3)

Estimate the solution to the system of equations.\newlineYou can use the interactive graph below to find the solution.\newline{y=4x−2y=x+3 \left\{\begin{array}{l} y=4 x-2 \\ y=x+3 \end{array}\right. \newlineChoose 11 answer:\newline(A) x=23,y=423 x=\frac{2}{3}, y=4 \frac{2}{3} \newline(B) x=123,y=323 x=1 \frac{2}{3}, y=3 \frac{2}{3} \newline(C) x=23,y=323 x=\frac{2}{3}, y=3 \frac{2}{3} \newline(D) x=123,y=423 x=1 \frac{2}{3}, y=4 \frac{2}{3}

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Q. Estimate the solution to the system of equations.\newlineYou can use the interactive graph below to find the solution.\newline{y=4x−2y=x+3 \left\{\begin{array}{l} y=4 x-2 \\ y=x+3 \end{array}\right. \newlineChoose 11 answer:\newline(A) x=23,y=423 x=\frac{2}{3}, y=4 \frac{2}{3} \newline(B) x=123,y=323 x=1 \frac{2}{3}, y=3 \frac{2}{3} \newline(C) x=23,y=323 x=\frac{2}{3}, y=3 \frac{2}{3} \newline(D) x=123,y=423 x=1 \frac{2}{3}, y=4 \frac{2}{3}
  1. Set Equations Equal: Set the equations equal to each other to find xx. 4x−2=x+34x - 2 = x + 3
  2. Solve for x: Solve for x x . 4x−x=3+2 4x - x = 3 + 2 3x=5 3x = 5 x=53 x = \frac{5}{3}
  3. Substitute xx into yy: Substitute x=53x = \frac{5}{3} into y=x+3y = x + 3 to find yy.
    y=(53)+3y = \left( \frac{5}{3} \right) + 3
    y=(53)+(93)y = \left( \frac{5}{3} \right) + \left( \frac{9}{3} \right)
    y=143y = \frac{14}{3}
  4. Check Solution: Check the solution in the other equation y=4x−2 y = 4x - 2 .
    y=4(53)−2 y = 4 \left( \frac{5}{3} \right) - 2
    y=203−2 y = \frac{20}{3} - 2
    y=203−63 y = \frac{20}{3} - \frac{6}{3}
    y=143 y = \frac{14}{3}
  5. Compare with Choices: Compare the solution (x,y)(x, y) with the given choices.
    (A) x=23,y=4(23)→y=83x = \frac{2}{3}, y = 4 \left( \frac{2}{3} \right) \rightarrow y = \frac{8}{3} (Incorrect)
    (B) x=123,y=323→x=53,y=113x = 1 \frac{2}{3}, y = 3 \frac{2}{3} \rightarrow x = \frac{5}{3}, y = \frac{11}{3} (Incorrect)
    (C) x=23,y=323→y=113x = \frac{2}{3}, y = 3 \frac{2}{3} \rightarrow y = \frac{11}{3} (Incorrect)
    (D) x=123,y=423→x=53,y=143x = 1 \frac{2}{3}, y = 4 \frac{2}{3} \rightarrow x = \frac{5}{3}, y = \frac{14}{3} (Correct)

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