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Solve using elimination.
{:[-7x-6y=16],[-8x-9y=-1]:}
(_____, _____)

Solve using elimination.\newline7x6y=168x9y=1 \begin{array}{l} -7 x-6 y=16 \\ -8 x-9 y=-1 \end{array} \newline(_____,_____)(\_\_\_\_\_, \_\_\_\_\_)

Full solution

Q. Solve using elimination.\newline7x6y=168x9y=1 \begin{array}{l} -7 x-6 y=16 \\ -8 x-9 y=-1 \end{array} \newline(_____,_____)(\_\_\_\_\_, \_\_\_\_\_)
  1. Write Equations: First, let's write down the system of equations we need to solve:\newline7x6y=16-7x - 6y = 16\newline8x9y=1-8x - 9y = -1\newlineWe want to eliminate one of the variables by making the coefficients of either xx or yy the same in both equations.
  2. Eliminate Variable: To eliminate yy, we can multiply the first equation by 99 and the second equation by 66 to get the coefficients of yy to be the same.\newlineMultiplying the first equation by 99:\newline(7x6y)×9=16×9(-7x - 6y) \times 9 = 16 \times 9\newline63x54y=144-63x - 54y = 144\newlineMultiplying the second equation by 66:\newline(8x9y)×6=1×6(-8x - 9y) \times 6 = -1 \times 6\newline48x54y=6-48x - 54y = -6
  3. New System: Now we have the new system of equations:\newline63x54y=144-63x - 54y = 144\newline48x54y=6-48x - 54y = -6\newlineWe can subtract the second equation from the first to eliminate y:\newline(63x54y)(48x54y)=144(6)(-63x - 54y) - (-48x - 54y) = 144 - (-6)\newline63x+48x=144+6-63x + 48x = 144 + 6\newline15x=150-15x = 150
  4. Subtract Equations: Now we can solve for xx by dividing both sides by 15-15:15x15=15015\frac{-15x}{-15} = \frac{150}{-15}x=10x = -10
  5. Solve for x: Now that we have the value of xx, we can substitute it back into one of the original equations to solve for yy. Let's use the first equation:\newline7x6y=16-7x - 6y = 16\newlineSubstitute x=10x = -10:\newline7(10)6y=16-7(-10) - 6y = 16\newline706y=1670 - 6y = 16
  6. Substitute xx: Now we can solve for yy by subtracting 7070 from both sides:\newline70706y=167070 - 70 - 6y = 16 - 70\newline6y=54-6y = -54
  7. Solve for y: Finally, we divide both sides by 6-6 to find the value of yy:6y6=546\frac{-6y}{-6} = \frac{-54}{-6}y=9y = 9