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Solve the system of equations. −8y+9x=−5-8y + 9x = -5 and 8y+7x=−758y + 7x = -75

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Q. Solve the system of equations. −8y+9x=−5-8y + 9x = -5 and 8y+7x=−758y + 7x = -75
  1. Combine equations: Add the two equations to eliminate the variable yy.
    −8y+9x=−5-8y + 9x = -5
    8y+7x=−758y + 7x = -75
    (−8y+9x)+(8y+7x)=−5+(−75)(-8y + 9x) + (8y + 7x) = -5 + (-75)
  2. Eliminate variable yy: Perform the addition to eliminate yy.
    −8y+8y+9x+7x=−5−75-8y + 8y + 9x + 7x = -5 - 75
    0y+16x=−800y + 16x = -80
    16x=−8016x = -80
  3. Solve for x: Solve for x by dividing both sides of the equation by 1616.\newline16x16=−8016\frac{16x}{16} = \frac{-80}{16}\newlinex=−5x = -5
  4. Substitute xx into equation: Substitute x=−5x = -5 into one of the original equations to solve for yy. We'll use the first equation −8y+9x=−5-8y + 9x = -5.
    −8y+9(−5)=−5-8y + 9(-5) = -5
    −8y−45=−5-8y - 45 = -5
  5. Isolate term with y: Add 4545 to both sides of the equation to isolate the term with y.\newline−8y−45+45=−5+45-8y - 45 + 45 = -5 + 45\newline−8y=40-8y = 40
  6. Solve for y: Solve for y by dividing both sides of the equation by -8＂).\(\newline\$-8y / -8 = 40 / -8\)\(\newline\)\(y = -5\)

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