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Solve using elimination.\newline5x−y=65x - y = 6\newline5x−3y=−125x - 3y = -12\newline(_____, _____)

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Q. Solve using elimination.\newline5x−y=65x - y = 6\newline5x−3y=−125x - 3y = -12\newline(_____, _____)
  1. Write Equations: Write down the system of equations to identify the strategy for elimination.\newline5x−y=65x - y = 6\newline5x−3y=−125x - 3y = -12\newlineWe can subtract one equation from the other to eliminate the variable xx.
  2. Subtract Equations: Subtract the first equation from the second equation to eliminate the variable xx.(5x−3y)−(5x−y)=−12−6(5x − 3y) − (5x − y) = −12 − 6 This simplifies to:5x−3y−5x+y=−12−65x − 3y − 5x + y = −12 − 6
  3. Combine Terms: Combine like terms.\newline−3y+y=−12−6-3y + y = -12 - 6\newline−2y=−18-2y = -18
  4. Solve for y: Solve for y by dividing both sides by -2＂).\(\newline\$-2y / -2 = -18 / -2\)\(\newline\)\(y = 9\)
  5. Substitute and Solve for \(x\): Substitute \(y = 9\) into one of the original equations to solve for \(x\). Using the first equation: \(5x − y = 6\) \(5x − 9 = 6\)
  6. Isolate x Term: Add \(9\) to both sides to isolate the term with \(x\).\(\newline\)\(5x - 9 + 9 = 6 + 9\)\(\newline\)\(5x = 15\)
  7. Final Solution: Divide both sides by \(5\) to solve for \(x\).\[\frac{5x}{5} = \frac{15}{5}\]\[x = 3\]

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