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Resca Posted on Mar 03, 2014
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Y>x^2-4x+3 solve by substitution

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k24674

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  • Posted on Mar 04, 2014
k24674
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You need to draw the curve y= x^2-4x+ 3. It is a parabola. The equality (=) is verified by all points on the curve. The curve divides the whole plane in two regions. In one region y will be less than x^2-4x+3. In the other regions y will be larger than x^2-4x+3
The regions are the interior of the parabola and its exterior. To find out the region where your inequality is verified you proceed as follow.

  1. Look at the graph and choose the coordinates of one point. Select integer values (BTW the point (0,0) is usually a good candidate) and write y ? x^2-4x+3 where the ? stands for the inequality sign you will have to insert to make the relation correct.
  2. Take x=0, and y=0 and substitute in y ? x^2-4x+3
  3. 0 ? (0^2)-4*(0)+3.
  4. Clearly the ? stands for < because 0 <3.
  5. So at all the points in the region where (0,0) is located the condition y< x^2-4x+3 is TRUE.
In the other region y < x^2-4x+3, is FALSE and that second region (the one that does not contain the origin (0,0) is the one you need to find. It represents your solution set. Note that the origin (0,0) does not lie in the solution set region

y>x^2-4x+3 - wereup0ohrv3gaaaabjru5erkjggg==

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How to solve equations with calculator
I'm not sure which calculator you are using, but the website desmos.com can be used as an online calculator. You would enter the two lines and where they intersect, it will tell you the coordinates.

Doing it manually, you could use the elimination or substitution method.

By the elimination method:

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A pair of running shoes costs $5.00 more than a pair of regular tennis shoes. The total cost for both is $115 Find the price of the regular tennis shoes
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