SOLUTION: Please help me with these problems 1. Find the equation in standard form,with all integer coefficients of the line perpendicular to x- 2y = 24 and passing through (1,3) 2.Sol

Algebra ->  Linear-equations -> SOLUTION: Please help me with these problems 1. Find the equation in standard form,with all integer coefficients of the line perpendicular to x- 2y = 24 and passing through (1,3) 2.Sol      Log On


   

Question 153499: Please help me with these problems
1. Find the equation in standard form,with all integer coefficients of the line perpendicular to x- 2y = 24 and passing through (1,3)
2.Solve the system of equation using the addition (elimination method)if the answer is a solution present it in ordered pair(x,y) if not specify wheather it a "no solution or "infinite many solution"
x + 2y = 5
3x + 4y = 1
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1. First find the slope of this line.
x-2y=24
-2y=24+-x
y=%2824-x%29%2F%28-2%29
y=%28x-24%29%2F2
The slope is (1/2).
Perpendicular lines have slopes that are negative reciprocals.
m%5B1%5Dm%5B2%5D=-1
%281%2F2%29m%5B2%5D=-1
m%5B2%5D=-2
Now use the point slope form of a line with the slope and point(1,3),
y-y%5B1%5D=m%28x-x%5B1%5D%29
y-3=-2%28x-1%29
y=-2x%2B2%2B3%29
y=-2x%2B5
Standard form
2x%2By=5

.
.
.
1.x+%2B+2y+=+5
2.3x+%2B+4y+=+1
Multiply eq. 1 by (-2) and add to eq. 2,
1.-2x+-4y+=+-10
2.3x%2B4y=1
-2x%2B3x-4y%2B4y=-10%2B1
x=-9
From 1,
1.x+%2B+2y+=+5
-9+%2B+2y+=+5
2y=14
y=7

One unique solution (-9,7).