SOLUTION: Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.
2x + 3y = 1
and 5x + 3y =16
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Question 105394: Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.
2x + 3y = 1
and 5x + 3y =16
x+5y = 10
and -2x – 10y = -20
Answer by elima(1433) (Show Source): You can put this solution on YOUR website!
Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.
2x + 3y = 1
and 5x + 3y =16
x+ 5y = 10
and -2x – 10y = -20
=================================
2x+3y=1
5x+3y=16
Multiply the first equation by -1;
(-1)2x+3y =1
-2x-3y=-1
================
now add the equations;
-2x-3y=-1
5x+3y=16
---------
3x=15
x=5
==============
2(5)+3y=1
10+3y=1
3y=-9
y=-3
So this equation has a solution, it is independent
===================================================
x+5y = 10
-2x – 10y = -20
=====================
lets multiply the first equation by 2;
(2)x+5y=10
2x+10y=20
===============
Now add the equations;
2x+10y=20
-2x=10y=-20
------------
0=0
dependent
:)
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