SOLUTION: Please help with this problem that is through a practice CD class. I know that it's probably not as hard as I'm making it. Solve for X and Y in the following problems and show

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Question 66146: Please help with this problem that is through a practice CD class. I know that it's probably not as hard as I'm making it.
Solve for X and Y in the following problems and show your work:
a. X + Y = 6; 2X + Y = 8
b. 7X + 3Y = 14; 5X + 9Y = 10
c. 4X + Y = 16; 2X + 3Y = 24
d. 12X + Y = 25; 8X - 2Y = 14
I appreciate your help.
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
X+Y=6 & 2X+Y=8 THEN X=6-Y FROM THE FIRST EQUATION. NOW SUBSTITUTE (6-Y) FOR X IN THE SECOND EQUATION THUS:
2(6-Y)+Y=8 & SOLVE FOR Y THUS:
12-2Y+Y=8 COMBINE THE Xs & SUBTRACT 12 FROM BOTH SIDES
-Y=8-12
-Y=-4 DIVIDE BOTH SIDES BY -1
Y=4 SOLUTION. NOW SUBSTITUTE 4 FOR X IN EITHER EQUATION THUS:
2X+4=8
2X=8-4
2X=4
X=4/2
X=2 SOLUTION
PROOF
X+Y=6
2+4=6
6=6
__________________________________________________________
7X+3Y=14 & 5X+9Y=10 MULTIPLY THE FIRST EQUATION BY -3 TO ELIMINATE THE Ys & ADD THEM
-21X-9Y=-42
5X+9Y=10
------------------------
-16X=-32
X=-32/-16
X=2 SOLUTION NOW SUBSTITUTE 2 FOR X IN EITHER EQUATION & SOLVE FOR Y
5*2+9Y=10
10+9Y=10
9Y=10-10
9Y=0
Y=0/9
Y=0
PROOF
7*2+3*0=14
14=14
----------------------------------------------------
4X+Y=16 & 2X+3Y=24 MULTIPLY THE FIRST EQUATION BY -3 & ADD TO ELIMINATE THE Ys.
-12X-3Y=-48
2X+3Y=24
-----------------------------
-10X=-24
X=-24/-10
X=2.4 SOLUTION. NOW SUBSTITUTE 2.4 FOR X & SOLVE FOR Y
4*2.4+Y=16
9.6+Y=16
Y=16-9.6
Y=6.4 SOLUTION.
PROOF
2*2.4+3*6.4=24
4.8+19.2=24
24=24
------------------------------------------------------
12X+Y=25 & 8X-2Y=14 MULTIPLY THE FIRST EQUATION BY 2 & ADD
24X+2Y=50
8X-2Y=14
-----------------
32X=64
X=64/32
X=23 SOLUTION NOW SUBSTITUTE 2 FOR X AND SOLCVE FOR Y
8*2-2Y=14
16-2Y=14
-2Y=14-16
-2Y=-2
T=-2/-2
Y=1 SOLUTION
PROOF
12*2+1=25
24+1=25
25=25