Question

Solving systems of equations through graphing
x + 2y = 10, I got (10,0)

3x + 4y = 8, I got (8/3,2)... How exactly do I graph this...?

Answer 1

Is this your system of equations?\[\rm x +2y = 10\\ 3x + 4y = 8\]

Answer 2

If this is, you need to graph two different lines on the same graph plane.

Answer 3

The easiest way to graph a line is to find the x-intercept, then find the y-intercept, then pass a line through the two points.

Answer 4

So if you have a linear equation, say, 6x + 2y = 18, then:

the x-intercept is (3,0)
the y-intercept is (0,9)

Mark these points and pass a line through them.

Answer 5

I know this... but how do I graph (8/3,2)?

Answer 6

That's neither the x-intercept nor the y-intercept.
Let's go step-by-step, okay?

Answer 7

Oh so I messed up?

Answer 8

Yup.

Answer 9

So, can you tell me what the x-intercept for x + 2y = 10 is?

Answer 10

10

Answer 11

Yeah, actually (10,0) because x = 10 and y = 0.
How about the y-intercept of x + 2y = 10?

Answer 12

5

Answer 13

(0,5) actually!

Answer 14

err sorry

Answer 15

So you have
(10,0)
and
(0,5)

mark them and pass a line thru.

Answer 16

You got one line, but you also gotta make a line for 3x + 4y = 8 right?

Answer 17

yes

Answer 18

Make the line for 3x + 4y = 8 on the SAME GRAPH PAPER.

Answer 19

so 3 * 0 + 4y = 8

Then 4y = 8 divide by 4 and I get y = 2 (0.2)

Answer 20

That's correct, and another point?

Answer 21

3x + 4 * 0 = 8
3x = 8 divide by 3 I get x = 8/3 (8/3, 0)

Answer 22

Very good! Now mark those points and pass a line thru.

Answer 23

How many lines do you have now?

Answer 24

one because I'm not sure how to graph (8/3,0)

Answer 25

lol

Answer 26

\[\rm \large {8 \over 3} = 2{2 \over 3}\]

Answer 27

So now do you get it?

Answer 28

yes

Answer 29

How many lines do you have now?

Answer 30

two

Answer 31

Great, and do those lines intersect?