Condition for infinite many solutions if two graph lines
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Answer:
You may have heard of infinity and beyond from a favorite toy adventurer...
...but we're not really talking about flying here. Instead, we're talking about systems of equations. Most systems of equations in Algebra 1 (where we are now) will have just one solution—just one set of variable values where all the equations are true. But some systems have infinite solutions.
How can systems have infinite solutions? If you solve a system with graphing, you might notice that the solution is where the lines cross. Let's look at a system of equations that has infinite solutions:
22x+11y=44
14x+7y=28
Try simplifying the top equation. What do you notice?
2x+y=4
2x+y=4
These are same equation! They'll both be exactly the same line on a graph. In other words, they'll overlap completely.
System of linear equations where the red line is 22x + 11y = 44 and the blue line is 2x + y = 4.
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Every point on the line will satisfy both equations. The line extends infinitely, so there are an infinite number of solutions.
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