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If -6x-9y=6 and -4x+y=-1 are true equations, what would be the value of -10x-8y ? Answer:

If −6x−9y=6 -6 x-9 y=6 and −4x+y=−1 -4 x+y=-1 are true equations, what would be the value of −10x−8y \mathbf{- 1 0 x}-\mathbf{8 y} ?\newlineAnswer:

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Q. If −6x−9y=6 -6 x-9 y=6 and −4x+y=−1 -4 x+y=-1 are true equations, what would be the value of −10x−8y \mathbf{- 1 0 x}-\mathbf{8 y} ?\newlineAnswer:
  1. Identify Equations: Identify the system of equations.\newlineWe have two equations:\newline11) −6x−9y=6-6x - 9y = 6\newline22) −4x+y=−1-4x + y = -1\newlineWe need to find the value of −10x−8y-10x - 8y.
  2. Solve for y: Solve the second equation for y.\newlineFrom equation 22) −4x+y=−1-4x + y = -1, we can express yy in terms of xx:\newliney=−1+4xy = -1 + 4x
  3. Substitute in Equation 11: Substitute the expression for yy into the first equation.\newlineReplace yy in equation 11) with the expression from the previous step:\newline−6x−9(−1+4x)=6-6x - 9(-1 + 4x) = 6
  4. Distribute and Simplify: Distribute and simplify the first equation.\newline−6x+9−36x=6-6x + 9 - 36x = 6\newlineCombine like terms:\newline−42x+9=6-42x + 9 = 6
  5. Solve for x: Solve for x.\newlineSubtract 99 from both sides:\newline−42x=−3-42x = -3\newlineDivide by −42-42:\newlinex=−3/−42x = -3 / -42\newlinex=1/14x = 1 / 14
  6. Substitute xx into yy: Substitute the value of xx back into the expression for yy.
    y=−1+4(114)y = -1 + 4(\frac{1}{14})
    y=−1+414y = -1 + \frac{4}{14}
    y=−1+27y = -1 + \frac{2}{7}
    y=−77+27y = -\frac{7}{7} + \frac{2}{7}
    y=−57y = -\frac{5}{7}
  7. Calculate −10x−8y-10x - 8y: Calculate the value of −10x−8y-10x - 8y using the found values of xx and yy.−10x−8y=−10(114)−8(−57)=−1014+407-10x - 8y = -10(\frac{1}{14}) - 8(-\frac{5}{7}) = -\frac{10}{14} + \frac{40}{7}
  8. Simplify Expression: Simplify the expression.\newlineFirst, simplify −1014-\frac{10}{14}:\newline−1014=−57-\frac{10}{14} = -\frac{5}{7}\newlineNow, add −57-\frac{5}{7} to 407\frac{40}{7}:\newline−57+407=357-\frac{5}{7} + \frac{40}{7} = \frac{35}{7}
  9. Convert to Whole Number: Convert the fraction to a whole number. 357=5\frac{35}{7} = 5

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