How do you graph the system x−4y≥−4 and 3x+y≤6?

1 Answer
Maggie
Feb 22, 2016

1) Graph the line y=14x+1,
it has a slope of 1/4 and a y intercept of 1.
2) The region x−4y≥−4 (or y≤14x+1) is the area below this line and the line itself, shade/hatch this region.

3) Graph the line y=−3x+6,
it has a slope of -3 and a y intercept of 6.
4) The region 3x+y≤6 (or y≤−3x+6) is the area below this line and the line itself, shade/hatch this region a different colour/pattern from the other region.

5) The SYSTEM, is the set of x and y values the satisfy both expressions. This is intersection of both regions. Whatever both shades occur is the graph of the system.

Explanation:

Consider the region defined by x−4y≥−4.
The edge of the region is defined by the equation x−4y=−4.
This need to be put in standard form.

Start with,
x−4y≥−4
Subtract x from both sides.
x−4y−x≥−4−x
Producing,
−4y≥−4−x.

Divide both side by -4 (remember to flip the inequality)
−4y−4≤−4−x−4.
We have
y≤1+x4 or y≤14x+1.
The edge is the line y=1/4 x + 1 and the region the area below this including the line.

Consider the region defined by 3x+y≤6.
The edge of the region is defined by the equation 3x+y=6.
This need to be put in standard form.

Start with,
3x+y≤6
Subtract 3x from both sides.
3x+y−3x≤6−3x
Producing,
y≤6−3x
or
y≤−3x+6

The edge is the line y=-3x+6 and the region the area below this including the line.

The SYSTEM, is the set of x and y values the satisfy both expressions. This is intersection of both regions.

Related questions
Impact of this question
2222 views around the world
You can reuse this answer
Creative Commons License