How do you graph the inequality 2x + 3y >6?

Question

The sum of two numbers is 35. Their difference is 11. What are the two numbers?
Solve the system by substitution.
3x – y = –7
x + y = –9
did everything else on homework....just need help with these..

Answer 1

Question 1
Consider the line 2x + 3y = 6
Points on the line are (0 , 2) and (3 , 0)
Draw a DOTTED line taking in these two points.
Now shade the region that lies ABOVE this dotted line.
Every point in this region will satisfy 2x + 3y > 6

Question 2
x + y = 35
x - y = 11
2x = 46
x = 23

23 + y = 35
y = 12

The numbers are 23 and 12

Question 3
y = - x - 9
3x - (- x - 9) = - 7
3x + x + 9 = - 7
4x = - 16
x = - 4

- 4 + y = - 9
y = - 5

x = - 4 , y = - 5

Answer 2

So you are asking for three questions.
To do the first one (2x + 3y > 6), we need to put the equation into slope-intercept form, which means y=Mx + B. M is the slope and B is the y intercept. Because the > (greater than) sign might be confusing, let's pretend that it is an equal sign (so that we can work out the equation).

2x + 3y > 6
3y > -2x + 6
y> -(2/3)x + 2

Now that we have our equation, how do we graph it? First of all we know that our y int is 2. So one point of the inequality is (0,2). To find our next point, we start at (0,2) and move 2 units down THEN 3 units to the right.

We can now graph the line because we have TWO points!

So we graph it but we have to make it dashed because THOSE POINTS ARE NOT INCLUDED. This is an inequality! :) So, draw the line with a ruler (DASHED).


The final step is to SHADE the inequality. Choose a test point (let's say (0,0) because it's better). There is a shortcut to do this really fast, but I won't explain now(email me). Now, if we plug it into the inequality, we get 0>2. Is it true? Nope! So, we take our pencil and shade in the REGION WITHOUT (0,0) up to the dashed line! We shade the side WITHOUT the point. And you're done! xD


Number two. To solve this, Let x= another number and y= the other number. If their sum is 35, then x + y = 35. If their difference is 11, then the equation will either be x - y = 11 or y - x = 11. It doesn't matter in this case but later on in Algebra 2 it will.
Solve the system:
x+y=35
x-y=11
2x = 46
x= 23

Substitute.
(23) + y = 35
y = 12

So the numbers are 23 and 12!
The last one is easy, don't worry!
Solve for y first.
3x - y = -7
-y = -3x - 7
y = 3x + 7

Now plug the equation into the bottom one:

x + y = -9
x + (3x + 7) = -9
4x + 7 = -9
4x = -16
x= -4

Substitute one more time:

x + y = -9
(-4) + y = -9
y = -5

To check this problem, simply plug in the x and y values.

x + y = -9
(-4) + (-5) = -9
-9 = -9

3x - y = -7
3(-4) - (-5) = -7
-12 + 5 = -7
-7 = -7

So, x = -4 and y = -5.

There you go! Hope you're done with your homework now! Enjoy the rest of the day.

*if you would like to learn a shortcut for the graphing inequalities just email me at [e-mail]
3x - y = -7
3(-3) -

Answer 3

1. Graph the line 2x + 3y = 6 as a dotted line to indicate that it is not part of the solution. (The = is not part of the inequality). Then choose any point not on the line, say, (0, 0). Substituting the x coordinate for x and the y-coordinate for y in the inequality, we get 0 + 0 > 6, which is false. So (0, 0) is on the wron side of the line. Shade the part of the plane on the other side of the line from (0, 0). That is your answer.

2. x + y = 35
x - y = 11

Add the left hand sides together and the right hand sides together.
2x = 46
so x = 23
using x + y = 35, y = 35 - 23 = 12.

3. Use the same trick
3x - y = -7
x + y = -9
so 4x = -16
and x = -4.
Thus, x + y = -4 + y = -9, and y = -5.

This works when one of the variables will drop out. If you get both variables when adding the left and right hand sides together, you need to multiply one or both equations by values so that the coefficient of one variable is the same except for sign in the two new equations.

Answer 4

Alrighgt for the solve the system by substitution one...

First u want to isolate one of the variables

i'll use the bottom one b/c its the easiest.

Subtract x from both sides:
y = -9 - x

Now that we know what y equals... substitute it into the other equation:
3x - y = -7 equates to 3x - (-9 - x) = -7

Now solve for x:

3x + 9 + x = -7

4x + 9 = -7

4x = -16

x = -4

So now that we know what x is, solve for y by plugging x into one of the equations. I will use the bottom equation once more b/c it is simpler.

x + y = -9

-4 + y + -9

y = -5

Now u can check by plugging x and y into the other equation and seeing if it comes out correctly:

3(-4) - (-5) = - 7

-12 + 5 does infact equal -7

So there u go :)

Answer 5

firstly give x=0 then y>2; give y=0 then x>3; take the bigger parts of x=3 apsis(right part of x=3); and take the upper part of y=2 oordinat; the connection area of these parts is your solution. for x=0 ; y=-1 for y=0; x=-1/3 now u have to draw a line which passes through y=-1and x=-1/3 . your solution is the area which s betveen coordinat system and your line.(it s a triangle)

Answer 6

3x - y = - 7
3x + 7 = y

x + y = - 9
y = - 9 - x

3x + 7 = - 9 - x
3x + x = - 9 - 7
4x = - 16
x = - 16 / 4
x = - 4

y = - 9 - (- 4)
y = - 9 + 4
y = - 5

Answer: x = - 4 and y = - 5

Proof (1st equation):
3(- 4) - (- 5) = - 7
- 12 + 5 = - 7
- 7 = - 7

Answer 7

x= -4 ( negative 4)
y= -5 (negative 5)