SOLUTION: Solve the following system of linear inequalities by graphing: x-2y<4 x<4

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Question 82579: Solve the following system of linear inequalities by graphing:
x-2y<4
x<4
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Solve the first equation for y:

Subtract x from both sides

Divide both sides by -2. Remember multiplying or dividing by a negative flips the inequality sign

Now graph both and

Lets pick a test point (0,0) and test it with

Plug in x=0, y=0

Since this expression is true we shade the entire region containing (0,0) for the inequality . This region is above the line.

Now lets test

Plug in x=0

Since this expression is true we shade the entire region containing (0,0) for the inequality . This is the region to the left of the vertical line.

Notice how these regions overlap. This overlapping region is our final shaded region. Every point in this region satisfies both and