SOLUTION: use substitution to solve each system of equations. if the system of equation does not have exactly one solution, state whether it has no solution or infinitely many solutions.

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Question 621498: use substitution to solve each system of equations. if the system of equation does not have exactly one solution, state whether it has no solution or infinitely many solutions.
x=3-2y
2x+4y=6
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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Solve the system of equations using the substitution method.
x=3-2y
2x%2B4y=6
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Substitute 3-2y for x in the second equation.
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2x%2B4y=6
2%283-2y%29%2B4y=6
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Simplify by clearing the parentheses.
6-4y%2B4y=6
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Combine like terms. Notice that -4y+4y=0, so we are left with 6=6.
When this happens, it means that the two equations in your system are actually equivalent. The graph of both equations is the same line.
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In this case, every point on the line is a solution to the system; we say that there are infinitely many solutions.
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Hope this helps! Feel free to email if you have questions about this.
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Ms.Figgy
math.in.the.vortex@gmail.com