Question

is (-4,7) the intersect of both lines when solving for x + 2y = 10, and 3x + 4y = 8?

Answer 1

This is solving systems of linear equations.
x + 2y = 10
3x + 4y = 8

Any idea how to go about this?

Answer 2

Yeah

x + 2y = 10
the answer is y = 5 (0,5) and x = 10 (10,0)

for 3x + 4y = 8 the answer is (0,2) for y and the slope is -3/4. I'm just wondering if (-4, 7) is the correct intersect on both lines

Answer 3

Oh... Graphing is a terrible way to solve systems, it's too... prone to human error. Here's an easier way :)
Substitute -4 for x, and 7 for y.
In the first equation
x + 2y = 10
substituting
-4 + 2(7) = 10

Is it valid?

Answer 4

-4 + 2 * 7 = 10 yes its true

Answer 5

Okay, so what does that tell you?
It tells you that the point (-4 , 7) is on the line
x + 2y = 10

But is it also on the line
3x + 4y = 8

?

Substitute and see.

Answer 6

3 * -4 + 4 * 7 = 8 false, the answer is 16

Answer 7

Then that can only mean that the point (-4, 7) is not on the line
3x + 4y = 8

What can you conclude now?

Answer 8

(-4,7) isn't going the intersect of both equations

Answer 9

Precisely :)

Answer 10

How do I find the intersect of both equations then?

Answer 11

Oh, well, let's go back to basics :D
Remember your properties of equality?

Answer 12

nope

Answer 13

Okay, let a, b, c, d be real numbers
If
a = b
then
ca = cb
correct?

Answer 14

yes

Answer 15

also, if
a = b
and c = d
Then
a + c = b + d

Right?
We just added the left sides and the right sides of the equations

Answer 16

yes

Answer 17

have you done metrics for 2x2 system it is a simple as solving by substitution

Answer 18

as simple as*

Answer 19

x + 2y = 10
3x + 4y = 8

We can add the left sides and the right sides, and it gives us
x + 3x + 2y + 4y = 18
4x + 6y = 18

But that's not really that helpful, is it? :P

Answer 20

have you learn substitution or elimination method?

Answer 21

This is the elimination method, by the way.

Answer 22

What do we do after we add both sides?

Answer 23

We don't. I'm just demonstrating adding both sides right away, and how useless it is :)

Now remember, that first property I showed you, where we multiply the same number on both sides of the equation?

Answer 24

Do you know what the problem I'm doing is called so I can find a video on www.khanacademy.org and see live examples?

Answer 25

Systems of Linear Equations.