Pair of lines: \determine point of intersection. Please tell me if I am correct.

[nukeman]

Homework Statement

Ok, I think i got it, but can you all tell me if these are the right/proper steps I must do?

Determine the point of intersection of the following pair of lines:

3x - 7y = 8
2x + 4y = -12

Now, first step is the use the 2nd equation and turn the 2nd equation into:

2x = -12 - 4y
x = -6 - 2y

THEN...subsitute the above date into the 1st equation)

3(-6 - 2y) - 7y = 8

turns into

-18 - 6y - 7y = 8 (just 3 x - 6 and 3 x -2y)

****now I go -6 + -7 = -13y and -18 - 8 = 26

so that then turns into:

-13y = 26

then

y = -2

Correct so far?

NOw for x, we go x = -6-2 (-2) = -2?

so x and y are both -2?

Are those the right steps? is there a better way? Am i correct?

Homework Equations

The Attempt at a Solution

 

[JonF]

if you ever want to check just plug x=-2 and y=-2 into your original equations

 

[nukeman]

Yes right, but are the steps I did correct?

 

[Mark44]

Does the point (-2, -2) satisfy both equations; i.e., make both equations true statements? If so, that means that this point is on both lines.

If you have found a point that is on both lines, then it's very unlikely that your steps are wrong.

BTW, your abilities have improved a lot in the last couple of weeks!

 

[nukeman]

Does the point (-2, -2) satisfy both equations; i.e., make both equations true statements? If so, that means that this point is on both lines.

If you have found a point that is on both lines, then it's very unlikely that your steps are wrong.

BTW, your abilities have improved a lot in the last couple of weeks!

Right. ye the both satisfy both equations.

Are the steps I did to solve t his correct? I know I got the right answer, but I want to make sure I am doing the steps 100% correct

 

[Mark44]

Yes, your work is correct. The point I'm making is that many times you can tell whether your work is correct by checking it. In this case, since x = -2 and y = -2 satisfy both equation, the point (-2, -2) is on both lines, and you have verified that the point you found is on both lines.

In that sense, algebra and other mathematics courses are different from, say, and English class, where you have to rely on an expert's judgment to determine whether what you have done is right. In mathematics you can be your own expert just by checking the result you found.