Question 496720: Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
6x – 4y = 19
24x - 16y = -76
can some one help me
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! This is a little bit of trick question. The answer is there are no solutions. But let me show you how we get there.
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The elimination method is about solving systems of equations by eliminating some of the terms (according to the rules of algebra) to get to a single term that can be easily calculated and then fed back into the system of equations to solve for the other unknown term. Two equations with two unknowns is pretty straightforward. Here's how we do it:
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6x - 4y = 19
24x - 16y = -76
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With equalities such as these, we can perform operations on the terms on one side of the "=" sign as long as we perform the same operation on the other side, thus preserving the basic equality relationship. So, for example, we could take the first equation and multiply both sides by 4:
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4 (6x - 4y) = 4 (19)
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which becomes:
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24x - 16y = 76
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But that looks a lot like the other equation:
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24x - 16y = -76
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By looking at this small but important difference in the two equations, we already know we have a solution problem. But we'll go ahead and use the elimination method to confirm it.
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So using the elimination method, we could add or subtract whole equations from one another in order to eliminate one of the variable (unknown) terms so we are left with a single variable (unknown) to solve for. However, IN THIS INSTANCE, because in both equations, all the terms on the left hand side of the "=" sign are the same, when we subtract one equation from the other, we will eliminate all of the x and y terms (not what we normally want):
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24x - 16y = 76
24x - 16y = -76
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As mentioned, if we subtract the 2nd equation from the first, all the x terms and y terms disappear and we are left with:
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0 = 76 - (-76)
0 = 152, which we know is false.
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So, there are no values of either x or y we can find that will ever satisfy this system of equations.
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cheers,
Lee
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