Question - Solving System of Linear Equations by Elimination
Solution:
To solve the system of linear equations using elimination, we can add the two equations together because the y terms are opposites and will cancel each other out. Here are the equations:1) $$ 4x + 2y = 14 $$2) $$ -5x - 2y = -16 $$Adding them together gives us:$$ (4x + 2y) + (-5x - 2y) = 14 + (-16) $$This simplifies to:$$ 4x - 5x + 2y - 2y = 14 - 16 $$$$ -x = -2 $$Now we can solve for x by dividing both sides by -1:$$ x = \frac{-2}{-1} $$$$ x = 2 $$With x found, we can substitute x = 2 into either of the original equations to solve for y. Using the first equation:$$ 4x + 2y = 14 $$Substituting 2 for x gives us:$$ 4(2) + 2y = 14 $$$$ 8 + 2y = 14 $$Subtract 8 from both sides to get:$$ 2y = 6 $$Divide by 2 to solve for y:$$ y = \frac{6}{2} $$$$ y = 3 $$So the solution to the system of equations is x = 2, y = 3.
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