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Solve using elimination.\newline−2x−5y=15-2x - 5y = 15\newline−2x−3y=1-2x - 3y = 1\newline(_____, _____)

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Q. Solve using elimination.\newline−2x−5y=15-2x - 5y = 15\newline−2x−3y=1-2x - 3y = 1\newline(_____, _____)
  1. Write Equations: Write down the system of equations.\newline−2x−5y=15-2x - 5y = 15\newline−2x−3y=1-2x - 3y = 1
  2. Eliminate xx: Since the coefficients of xx in both equations are the same but with opposite signs, we can eliminate the xx variable by subtracting the second equation from the first.\newline(–2x−5y)−(–2x−3y)=15−1(–2x − 5y) − (–2x − 3y) = 15 − 1
  3. Subtract Equations: Perform the subtraction to eliminate the xx variable. −2x+2x−5y+3y=15−1\,-2x + 2x - 5y + 3y = 15 - 1
  4. Simplify Result: Simplify the resulting equation.\newline0x−2y=140x - 2y = 14
  5. Solve for y: Solve for y.\newline−2y=14-2y = 14\newliney=14(−2)y = \frac{14}{(-2)}\newliney=−7y = -7
  6. Substitute and Solve: Substitute the value of yy back into one of the original equations to solve for xx. We can use the second equation for this purpose.\newline−2x−3(−7)=1-2x - 3(-7) = 1
  7. Final Solution: Simplify the equation and solve for xx.\newline–2x+21=1–2x + 21 = 1\newline–2x=1−21–2x = 1 − 21\newline–2x=−20–2x = −20\newlinex=−20/(−2)x = −20 / (−2)\newlinex=10x = 10

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