Point of Intersection (fractions)

[H8Math]

my homework asks that i find the point of intersection of each of the given pairs of straight lines. i think i understand the concept and have used the elimination and substitution methods to isolate x, but i can't seem to get the answer the book gives (-4,-6). i'm sure i'm missing a mathmatical procedure regarding the fractions. could someone help me work this out?

y = 1/4x - 5
2x - 3/2y = 1

substitution:

2x - 3/2 (1/4x - 5) = 1
i then distribute the 3/2 and get
2x - 3/8x - 15/2 = 1
then it goes bad...

i've also done elimination:
but that's a bit complicated to type out. i'll enter it if it's necessary.

on my own, i've gotten answers ranging from negative numbers (-2/3) to 318...HELP! :?

 

[stapel]

y = 1/4x - 5
2x - 3/2y = 1

If the fractions are a problem, get rid of them. :wink:

What you have posted means the following:

. . . . .y = 1/(4x) - 5
. . . . .2x - 3/(2y) = 1

...but I will assume that you actually mean this:

. . . . .y = (1/4)x - 5
. . . . .2x - (3/2)y = 1

Multiply the first equation by 4 and the second by 2:

. . . . .4y = x - 20
. . . . .4x - 3y = 2

Rearrange:

. . . . .-x + 4y = -20
. . . . .4x - 3y = 2

Multiply the first equation by 4:

. . . . .-4x + 16y = -80
. . . . .4x - 3y = 2

Add down to get "13y = -78", solve for y, and then back-solve for x. :idea:

Have fun!

Eliz.