Solve each system of inequalities

Question

Solve each system of inequalities

Y>=x+4

Y <2x-1

 

Answer 1

Hi Melisa, start by plotting the two lines.

 

y ≥ x + 4:

 

The line to plot is y = x + 4.

 

Find some points:

 

x = 0, y = 4

 

x = -1, y = 3

 

x = 1, y = 5

 

This line goes from lower left to upper right.

 

The inequality says everything on the line or greater than the line satisfies the inequality.

 

y < 2x - 1:

 

The line to plot is y = 2x -1.

 

Find some points:

 

x = 0, y = -1

 

x = -1, y = -3

 

x = 1, y = 1

 

The line goes from lower left to upper right, similar to the first line, but with a different slope.

 

The inequality say every thing below the line satisfies the inequality.

 

If we extend the two lines, we see they will cross at a point, (5, 9) and continue on. The area above or on the first line and below the second line is the wedge starting at the point (5, 9) and extending up and to the right in the first quadrant. This is the solution to the system of inequalities.

 

We can find the point where the two line intersect by solving the following system of equations:

 

y =   x + 4

y = 2x  - 1

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The solution is the point (5, 9).

 

Questions?