# System ot 2 linear inequalities

### System ot 2 linear inequalities

Does someone knows which are the answers of the system
|x + y < 4
|2x + 5y > 10
student

### Re: System ot 2 linear inequalities

We simply solve the above equation to find the values of x and y.
2x + 5y > 10
x + y < 4

2x + 5y >= 10
x + y <= 4
Multiplying second equation with 2 we get:

2x + 2y <= 8

Solving both the equations we get:
3y = 2
y = 2/3

Now put the value of y in second equation:
y = 4 - 2/3
= 10/3

Jessica

Posts: 12
Joined: Mon Aug 20, 2012 7:31 am
Reputation: 3

### Re: System ot 2 linear inequalities

The problem with Jessica's answer is that these are NOT equations.

The first inequality is 2x+ 5y< 10. The equation 2x+ 5y= 10 gives the boundary line to the region of (x, y) pairs that satisfy the inequality. When x= 0, 5y= 10 so y= 2. (0, 2) is one point on that line. When y= 0, 2x= 10 so x= 5. (5, 0) is another point on that line. The equation 2x+ 5y= 20 gives the line through (5, 0) and (0, 2). Since (0, 0) makes 2x+ 5y= 0< 10, the set of points (x, y) that satisfy 2x+ 5y> 10 are the points on the other side of that line.

The other inequality is x+ y< 4. The equation x+ y= 4 gives the boundary line of the region of (x, y) pairs that satisfy the inequality. When x= 0, y= 4 so (0, 4) is one point on that line. When y= 0, x= 4 so (4, 0) is another point on that line. The equation x+ y= 4 gives the line through (4, 0) and (0, 4). Since (0,0) makes x+ y= 0< 4 the set of points that satisfy x+ y<4 are that side of the line.

The two lines 2x+ 5y= 10 and x+ y= 4 cross at x+ y= 4 and divide the pLane into 4 region:
The points above both lines and satifying 2x+ 5y> 10 and x+ y> 4.
The points above 2x+ 5y= 10 and below x+ y= 4 and satisfying 2x+ 5y> 10 and x+ y< 4.
The points below 2x+ 5y= 10 and under x+ y= 4 and satisfying 2x+ 5y< 10 and x+ y> 4.
The points below both liness and satisfying both 2x+ 5y< 10 and x+ y< 4

The best way to show the region is to graph the two lines and shade the correct regions.
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