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Solve the system of equations. {:[7x-3y=20],[y=5x-4],[x=◻],[y=◻]:}

Solve the system of equations.\newline7x−3y=20y=5x−4x=□y=□ \begin{array}{l} 7 x-3 y=20 \\ y=5 x-4 \\ x=\square \\ y=\square \end{array}

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Full solution

Q. Solve the system of equations.\newline7x−3y=20y=5x−4x=□y=□ \begin{array}{l} 7 x-3 y=20 \\ y=5 x-4 \\ x=\square \\ y=\square \end{array}
  1. Substitute yy into first equation: Substitute yy from the second equation into the first equation.\newlineWe have y=5x−4y = 5x - 4. Substitute this into 7x−3y=207x - 3y = 20.\newline7x−3(5x−4)=207x - 3(5x - 4) = 20
  2. Distribute and simplify: Distribute the −3-3 across the parentheses and simplify.7x−15x+12=207x - 15x + 12 = 20−8x+12=20-8x + 12 = 20
  3. Isolate the variable x: Isolate the variable x.\newline−8-8x + 1212 - 1212 = 2020 - 1212\newline−8-8x = 88
  4. Solve for x: Solve for x.\newline−8x=8-8x = 8\newlinex=8−8x = \frac{8}{-8}\newlinex=−1x = -1
  5. Substitute xx back into second equation: Substitute xx back into the second equation to solve for yy.
    y=5x−4y = 5x - 4
    y=5(−1)−4y = 5(-1) - 4
    y=−5−4y = -5 - 4
    y=−9y = -9
  6. Write the solution as an ordered pair: Write the solution as an ordered pair.\newlineThe solution is (x,y)=(−1,−9)(x, y) = (-1, -9).

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