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Solve the system of equations using elimination: 2x+3y=-14 and x+5y=0

Solve the system of equations using elimination: 2x+3y=−14 2 x+3 y=-14 and x+5y=0 x+5 y=0

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Q. Solve the system of equations using elimination: 2x+3y=−14 2 x+3 y=-14 and x+5y=0 x+5 y=0
  1. Write Equations: Write down the system of equations.\newline2x+3y=−142x + 3y = -14\newlinex+5y=0x + 5y = 0
  2. Multiply and Set Up: Multiply the second equation by −2-2 to set up for elimination of xx.−2(x+5y)=−2(0)-2(x + 5y) = -2(0)−2x−10y=0-2x - 10y = 0
  3. Eliminate x: Add the modified second equation to the first equation to eliminate x.\newline(2x+3y)+(−2x−10y)=−14+0(2x + 3y) + (-2x - 10y) = -14 + 0\newline2x−2x+3y−10y=−142x - 2x + 3y - 10y = -14\newline0x−7y=−140x - 7y = -14
  4. Solve for y: Solve for y.\newline−7y=−14-7y = -14\newliney=−14−7y = \frac{-14}{-7}\newliney=2y = 2
  5. Substitute and Find xx: Substitute y=2y = 2 into the second original equation to find xx.x+5(2)=0x + 5(2) = 0x+10=0x + 10 = 0x=−10x = -10
  6. Write Ordered Pair: Write the solution as an ordered pair (x,y)(x, y).\newlineThe solution is (−10,2)(-10, 2).

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