how do I graph these equations 2x + 3y = 6, 2x - 3y = 12?

Answer 1

Hello, I come form Hong Kong. This equations is too easy.
You can use three methods to solve this question.
2x+3y=6-----------1
2x-3y=12----------2
2x(2)-3y(2)=6(2)----------3
2x-3y=12---------------4
4x-6y=12
-) 2x-3y=12

2x-3y=0
2x=3y

put(2x=3y) into 1

3y+3y=6
6y=6
y=1
put y=1 into 1

2x+3(1)=6 2x+3=6
2x=3 x=1.5

Don't forget your question is 2x + 3y = 6, 2x - 3y = 12
Thus don't let x=0 y=2

If you know that y=1 and x=1.5
You can know how to graph these equations.
Hope this answer can help you


If u want to graph this equation, u should use graph papper.

Answer 2

First you must put it in a graphable form, so you need to have somehting of the form mx +b=y

so the first one is 2x-6=-3y, which simplifies to -2/3x - 2 = y (simplify the equation by subtracting and adding to the different sides, so that y is on one side, and everything else is on the other, then divide everything (including the y) by the number in front of the y (remember if there is no number than it is a 1) then, the equation is simplified)

For this, draw a graph, and then next to it make a table.
In the table, have two collumns, x, and y.
So first choose a number for x, lets say 3. then multiply by -2/3s (you get -2), subtract two, and you get y(which in this case is -4).
Put one dot on the graph, at 3 on the x axis(side to side), and -4 on the y axis (up and down).

then choose another number (multiples of threes would be easiest, since you have to multiply by -2/3s, but any number works) lets say 6, which, when plugged into the equation gets us -2/3*6 - 2 = y. which means that y equals -6. on the graph, put a point that at 6 on the x axis, and 6 on the y.

Draw a line through these two points, and you have graphed the equation

do the same thing with the second equation, following the steps in order. (hint, the second equation simplifies to 2/3x-4=y)

best,
taygrin

Answer 3

2x + 3y = 12 y = ( - 2x + 12)/3 equation of the line m = slope = -2/3 you can plug in two numbers so you can draw a line through the two points. you can do it by choosing two numbers for X. lets say when x = 0 y = 12/3 = 4 and when x = 3 y = - 2 + 4 = 2 therefore you have coordinates on the graph: (0, 4) and (3, 2) find the above coordinates and draw a line through them

Answer 4

1. 2x + 3y = 6
*Write the equation in slope-intercept form: y = mx + b

First: subtract "2x" from both sides...

2x - 2x + 3y = 6 - 2x
3y = 6 - 2x

Sec: isolate "y" on one side > divide each term by "3"...

3y/3 = 6/3 - 2x/3
y = 2 - (2/3)x

Third: the equation has to be in alpha descending order...

y = (- 2/3)x + 2

*Graph the y-intercept "2" first, then graph the slope "-2/3" (rise over run)

2. 2x - 3y = 12

First: subtract "2x" from both sides...

2x - 2x - 3y = 12 - 2x

- 3y = 12 - 2x

Sec: isolate "y" > divide each term by "-3"...

- 3y/-3 = 12/-3 - (2/-3)x
y = - 4 - (-2/3)x
y = - 4 + (2/3)x

Third: alpha descending order...

y = (2/3)x - 4

*graph the y-intercept "4" first, & graph the slope "2/3" (rise over run)

Answer 5

the easiest way is to find the x-y intercepts of each linear equation by letting x or y be equal to 0.

for 2x+3y=6 let y=0 then x=3 the x int is (3,0)
let x=0 then y=2 the y int is (0,2)
plot the points and connect them.

do the steps again for the next equation.

Answer 6

If you sub in any x value, or any y value, it will give you a corresponding value 4 y or x respectively. If you plot a variety of these points it will give you an idea of the shape of the line

EG, EQ.1
If x=0, 3y=6, y=2, a point on the graph is (0,2)

Answer 7

First you need to put them in slope intercept form
Which would be y = -2/3x + 2 and y = 2/3x - 4

Then you go to your graph and plot 2 on the y axis, then down 2 over 3 put a dot and possibly do it again, then go to -4 on the y axis and go up 2 and over 3, connect your dots.
Hope this helps.

Answer 8

Make x/y charts (one for each equation). Set x as -1, 0 & 1. Solve for y and put the y into the chart. Then you`ll have your points and you can just graph the line. You can also use y=mx+b (y-intercept from). For those equations, the way I said would probablly be easier.

Answer 9

Put them both in slope-intercept form:
3y=-2x+6
y=-2/3x+2

-3y=-2x+12
y=2/3x-4

Just plug in numbers for x to get the y-values. Here's an example:
y=-2/3(9/2)+2
y=-3+2
y=-1

y=2/3(9/2)-4
y=3-4
y=-1

The intersection point is at (9/2,-1)

The y-intercepts:
y=-2/3(0)+2
y=2
(0,2)

y=2/3(0)-4
y=-4
(0,-4)

The x-intercepts:
0=-2/3x+2
-2/3x=-2
x=-2(-3/2)
x=3
(3,0)

0=2/3x-4
-2/3x=-4
x=-4(-3/2)
x=6
(6,0)

I hope this helps!

Answer 10

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

2x + 3y = 6
2x - 3y = 12

This will graph it for you.