SOLUTION: Please help I believe these problems fall into the above catagory. 4. 7x – 2y = 8 -14x + 4y = 8 5. 7x – 2y = 8 -14x + 4y = -16 Solve the inequality: 3x – 2.5y = 7.

Algebra ->  Graphs -> SOLUTION: Please help I believe these problems fall into the above catagory. 4. 7x – 2y = 8 -14x + 4y = 8 5. 7x – 2y = 8 -14x + 4y = -16 Solve the inequality: 3x – 2.5y = 7.      Log On


   



Question 176174: Please help I believe these problems fall into the above catagory.
4. 7x – 2y = 8
-14x + 4y = 8
5. 7x – 2y = 8
-14x + 4y = -16
Solve the inequality:
3x – 2.5y = 7.125
2.5x - 3y = 7.3125


Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.7x-2y=8
2.-14x%2B4y=8
Double eq.1 and add to eq. 2 to get rid of x.
2%287x-2y%29%2B%28-14x%2B4y%29=2%288%29%2B8
14x-4y-14x%2B4y=16%2B8
0=24
Inconsistent system, there is no solution.
These are two parallel lines that never meet, hence no solution.

.
.
.
3.7x-2y+=+8
4.-14x%2B4y+=+-16
Double eq.3 and add to eq. 4 to get rid of x.
2%287x-2y%29%2B%28-14x%2B4y%29=2%288%29-16
14x-4y-14x%2B4y=16-16
0=0
Consistent, dependent system, there are infinite solutions.
These two lines are actually the same line. So all of the points on the line solve this system of equations.
+graph%28+300%2C+300%2C+-5%2C+5%2C+-10%2C+10%2C+%288-7x%29%2F%28-2%29%29+
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.
.
5.3x-2.5y=7.125
6.5x+-+3y+=+7.3125
Let's multiply eq. 5 by 5 and eq. 6 by 3,then subtract to get rid of x.
5%283x-2.5y%29-3%285x-3y%29=5%287.125%29-3%287.3125%29
15x-12.5y-15x%2B9y=35.625-21.9375
-3.5y=13.6875
Change both left and right hand sides to a fractions before continuing,
-%287%2F2%29y=13%2B11%2F16
-%287%2F2%29y=208%2F16%2B11%2F16
-%287%2F2%29y=219%2F16
y=-219%2F16%2A%282%2F7%29
y=-219%2F16%2A%282%2F7%29
y=-219%2F56
From eq. 6,
6.5x+-+3y+=+7.3125
5x-3%28-219%2F56%29=7%2B5%2F16
5x%2B657%2F56=7%2B5%2F16
5x%2B657%2F56=112%2F16%2B5%2F16
5x%2B657%2F56=117%2F16
5x=117%2F16-657%2F56
5x=%28117%2F16%29%287%2F7%29-%28657%2F56%29%282%2F2%29
Common denominator is 112.
5x=819%2F112-1314%2F112
5x=-495%2F112
x=-99%2F112

or approximately,
x=-.89
y=-3.91