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Solve using elimination.\newline5x8y=25x - 8y = 2\newline7x+8y=10-7x + 8y = 10\newline(_____, _____)

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Q. Solve using elimination.\newline5x8y=25x - 8y = 2\newline7x+8y=10-7x + 8y = 10\newline(_____, _____)
  1. Set Up Equations: First, we need to set up the equations to eliminate one of the variables. We have the following system of equations:\newline5x8y=25x − 8y = 2\newline7x+8y=10−7x + 8y = 10\newlineWe can see that the coefficients of yy are opposites, which means we can add the two equations together to eliminate the yy variable.
  2. Add Equations: Now, let's add the two equations together:\newline(5x8y)+(7x+8y)=2+10(5x − 8y) + (−7x + 8y) = 2 + 10\newlineThis simplifies to:\newline5x7x=125x − 7x = 12
  3. Combine Like Terms: Next, we combine like terms: 2x=12-2x = 12
  4. Solve for x: Now, we solve for x by dividing both sides by 2-2:\newlinex=122x = \frac{12}{-2}\newlinex=6x = -6
  5. Substitute x Value: With the value of xx found, we can substitute x=6x = -6 into one of the original equations to find the value of yy. We'll use the first equation:\newline5x8y=25x − 8y = 2\newline5(6)8y=25(-6) − 8y = 2
  6. Perform Multiplication: Now, we perform the multiplication:\newline308y=2-30 − 8y = 2
  7. Isolate y Term: Next, we add 3030 to both sides to isolate the term with yy: \newline8y=2+30-8y = 2 + 30\newline8y=32-8y = 32
  8. Solve for y: Finally, we divide both sides by 8-8 to solve for yy:y=328y = \frac{32}{-8}y=4y = -4

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