graph and solve 4x+2y< or = to 16 and x+y > or equal to 5?

Answer 1

Graph the inequalities as you would graph a line.

For 4x + 2y ≤ 16, plot the x-intercept. (This is the point where the line crosses the x-axis.)

On the x-axis, the y-coordinate is 0, so for all intents and purposes, you have 4x = 16, and the x-intercept is 4.

Now plot the y-intercept. The x-coordinate is zero and drops out of the equation. You have 2y = 16 or y = 8. The y-intercept is 8.

Now that you know the intercepts, draw a line through these two points. Because the inequality is "≤," draw a solid line to indicate the points on the line are in the solution set.

The line divides the xy-plane into two regions, one of which contains the solutions to your inequality and one doesn't. Pick any point not on the line and test it. (I like choosing the origin anytime I can, because zero's are easy to work with!) When you substitute (0,0) into 4x + 2y ≤ 16, you get
0 + 0 ≤ 16, which is a true statement. This means any point on this side of the line will satisfy the inequality. Shade this region very lightly.

Now do the same with x + y ≥5. The intercepts are x = 5 and y = 5, and draw a line through these two points. Once again, it will be a solid line. (If your inequality is strictly < or >, without the =, then you'd use a dotted line.)

Again, find which side of this line is the correct region to satisfy the inequality.
Picking (0,0), you have 0 + 0 ≥ 5, which is a FALSE statement, meaning you've chosen the incorrect side of the line. Lightly shade the other side.

The system of inequalitites
4x + 2y ≤ 16 and x + y ≥ 5
has an infinite number of solutions, but they're easily represented by your graph. You have two lines drawn, separating the plane into four regions, but only one of them satisfies both inequalities. Shade this region a little darker to distinguish it from the rest.
The solution set will include the point (3,2) and every point in the region up and to the left from that point that's bounded by the two lines you drew.

Answer 2

its kind of hard to display graphs on here but I could help you to solve the equations.

first bring y to one side in both equations.
you get:

y >= 5 - x
y <= 8 - 2x

Then you can graph them and see where the two inequalities are equal or you can compare the two inequalities and see the common ranges.

Answer 3

4x+2y 2y y
x+y>/=5
y>/=5-x

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Answer 4

for a graph, go to www.quickmath.com, click in Plot under Inequalities, then click Advanced, type in

4x + 2y <= 16
x + y >= 5