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Course: Digital SAT Math > Unit 10
Lesson 8: Graphs of linear systems and inequalities: advancedGraphs of linear systems and inequalities — Basic example
Watch Sal work through an easier graphs of linear systems and inequalities problem.
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- This is hard ngl(31 votes)
- If you're writing the DSAT, it would be better if you used the graphing calculator. It makes it easier. Some calculator apps have graphing calculators, especially the ones on laptops.(16 votes)
- Just watch the sign . If y is <= mx+b then we should shade in lower region from the boundary of line .
same as If y is >= mx+b then we should shade in upper region from the line boundary . After shading both region check the overlapping region which contain both shaded region of two line . Basically that region is the solution for both inequalities.
If you still don't understand then I recommend you to check the Things to remember section of previous page where you can get the concepts.(16 votes)
- I get confused how to identify the upper and lower part(8 votes)
- Just do more practice and make sure to watch the videos on the lesson prep, it really helps, goodluck btw!!(7 votes)
- i think i got this(9 votes)
- What if the inequality is a vertical line: y </>/>=/<=(infinity)x?(7 votes)
- I don't think this type of questions will ever be on SAT, but if the inequality is a vertical line, it'll either fbe the left side or the right side. For example, x≥1 is a vertical line, with the right hand side of the line included. Try experimenting on graphing calculators (like Desmos) and play around with it!(2 votes)
- this is very confusing and i really don't understand I am getting stressed rn(6 votes)
- y>-3x+3.the shaded line will be the greater side of the inequality.It is better to do with example (1,0).... and use a graph paper/do normally with points.
Take a point on the line and move the point along y axis you will know outside the shaded region all values of y are smaller than inside shaded region(1 vote)
- cant we just use desmos for it?(2 votes)
- You could use Desmos, but it is better to learn how to solve the equation without a graphing calculator, as it strengthens your brain in problem solving.(7 votes)
- How is Sal determining which region would be included?(2 votes)
- Basically, if you see the > sign on an inequality it tells you that you shade the region above the line whereas if you see the < sign on the inequality it tells you that you should shade the region below the line.(6 votes)
- Here's a Life saving tip about which region to shade . Just forget that if y is greater than or less than mx+b and to shade the above or the belove region , Look at this :
if you have two inequalities , consider :
y >= -3x + 3 & y<=2x-2
1-Now Isolate x and y on one side.
2-first put x= 0 , it will give you the value of y.
3- Then put y = 0, It will give you the value of x.
like :
y+3x = 3 ---> (∵ x= 0) ---> y = 3 , similarly
y+3x = 3 ---> (∵y = 0) ---> x = 1 .....Do the same with the second equation.
4 - Plot The four vertices (points) obtained by solving the inequalities on the graph ..
5- Now it comes to shading . For that Similarly isolate x and y on one side and then put x = 0 and y = 0 ... If the inequality proves True Shade the region towards the origin (i.e (0,0)) and if The inequality proves false Shade the region in opposite direction to the origin of both inequalities .
y+3x >= 3 ---> (∵ x= 0, y=0) ---> 0 >= 3 (false)
y - 2x <=-2 ---> (∵ x= 0, y=0) ---> 0<=2 (false)
SO BOTH WILL BE SHADED IN OPPOSITE DIRECTION TO ORIGIN.
6 - Then the common region where both lines' shading meet will be our shaded region..(3 votes) - How is Sal determining which region would be included?(0 votes)
- if y>mx+c, the upper part of the line is to be shaded and if y<mx+c, shade the lower part of the line.(5 votes)