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If 9x-10y=7 and -x-9y=6 are true equations, what would be the value of -10x+y ? Answer:

If 9x−10y=7 \mathbf{9 x}-\mathbf{1 0 y}=\mathbf{7} and −x−9y=6 -\mathbf{x}-\mathbf{9 y}=\mathbf{6} are true equations, what would be the value of −10x+y -\mathbf{1 0 x}+\mathbf{y} ?\newlineAnswer:

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Q. If 9x−10y=7 \mathbf{9 x}-\mathbf{1 0 y}=\mathbf{7} and −x−9y=6 -\mathbf{x}-\mathbf{9 y}=\mathbf{6} are true equations, what would be the value of −10x+y -\mathbf{1 0 x}+\mathbf{y} ?\newlineAnswer:
  1. Equations to Solve: We have two equations:\newline11) 9x−10y=79x - 10y = 7\newline22) −x−9y=6-x - 9y = 6\newlineWe need to find the value of −10x+y-10x + y. To do this, we can solve the system of equations for xx and yy and then substitute these values into the expression −10x+y-10x + y.
  2. Isolate xx: First, let's solve for xx using the second equation. We can do this by isolating xx on one side of the equation.\newline−x−9y=6-x - 9y = 6\newlineMultiply both sides by −1-1 to get xx by itself:\newlinex=9y−6x = 9y - 6
  3. Substitute xx into 11st equation: Now that we have xx in terms of yy, we can substitute this expression for xx into the first equation to solve for yy.
    Substitute x=9y−6x = 9y - 6 into the first equation:
    9(9y−6)−10y=79(9y - 6) - 10y = 7
  4. Solve for y: Next, we expand the equation and simplify it to solve for y. \newline81y−54−10y=781y - 54 - 10y = 7\newlineCombine like terms:\newline71y−54=771y - 54 = 7\newlineAdd 5454 to both sides:\newline71y=6171y = 61\newlineDivide both sides by 7171:\newliney=6171y = \frac{61}{71}
  5. Substitute yy into xx expression: Now that we have the value of yy, we can substitute it back into the expression for xx to find the value of xx.
    x=9y−6x = 9y - 6
    x=9(6171)−6x = 9(\frac{61}{71}) - 6
  6. Calculate x value: We calculate the value of x by multiplying 99 by 61/7161/71 and then subtracting 66.
    x=549/71−6x = 549 / 71 - 6
    To subtract 66, we need to express it as a fraction with the same denominator as 549/71549/71:
    x=549/71−426/71x = 549 / 71 - 426 / 71
    x=(549−426)/71x = (549 - 426) / 71
    x=123/71x = 123 / 71
  7. Substitute xx and yy into expression: Finally, we substitute the values of xx and yy into the expression −10x+y-10x + y to find the value we're looking for.\newline−10x+y=−10(123/71)+(61/71)-10x + y = -10(123 / 71) + (61 / 71)
  8. Substitute xx and yy into expression: Finally, we substitute the values of xx and yy into the expression −10x+y-10x + y to find the value we're looking for.\newline−10x+y=−10(123/71)+(61/71)-10x + y = -10(123 / 71) + (61 / 71) We calculate the value of −10x+y-10x + y by multiplying −10-10 by 123/71123/71 and then adding 61/7161/71.\newlineyy00\newlineCombine the fractions:\newlineyy11\newlineyy22

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