SOLUTION: how to solve by substitution? problems: 1) x + y = -6 and 3x - 3y = -18 2) - 4x + 2y = 10 and 8x - 8y = -16 3) -6x + 4y = 2 and 6x - 2y = -10

Algebra ->  Test -> SOLUTION: how to solve by substitution? problems: 1) x + y = -6 and 3x - 3y = -18 2) - 4x + 2y = 10 and 8x - 8y = -16 3) -6x + 4y = 2 and 6x - 2y = -10      Log On


   

Question 465399: how to solve by substitution?
problems:
1) x + y = -6 and 3x - 3y = -18
2) - 4x + 2y = 10 and 8x - 8y = -16
3) -6x + 4y = 2 and 6x - 2y = -10
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1)
+3x+-+4y+=+-30........1
-5x+-2y+=+-22.........2......both sides multiply by -2
------------------------------------
-5x%28-2%29+-2y%28-2%29+=+-22%28-2%29.........2
10x+%2B4y+=+44.....2....add to 1
--------------------------------------
+3x+-4y+=+-30........1
10x+%2B4y+=+44..........2
--------------------------------------
+3x%2B10x+-4y%2B4y+=+-30%2B44
+13x+-cross%284y%29%2Bcross%284y%29+=+14
+13x=+14
+x=+14%2F13
+highlight%28x=+1.08%29
+3x+-4y+=+-30........1.plug in +x=+1.08
+3%281.08%29+-4y+=+-30
+3.24+%2B30+=+4y
+33.24+=+4y
+y=33.24%2F4
+highlight%28y=8.31%29

check:
+3x+-4y+=+-30........1
+3%281.08%29+-4%288.31%29+=+-30
+3.24+-33.24+=+-30
+-30+=+-30

2)
-6x+-+6y+=+-18........1
-4x+-+3y+=+-11........2.....both sides multiply by -2
--------------------------
-4x%28-2%29+-3y%28-2%29+=+-11%28-2%29
8x+%2B6y+=+22................add to 1
-------------------------------
-6x+-+6y+=+-18........1
8x+%2B6y+=+22...........2
---------------------------
-6x+%2B8x-+6y%2B6y+=+-18%2B22

2x=+4
highlight%28x=+2%29
-4%2A2+-+3y+=+-11........2.
-8+%2B11+=+3y
3+=+3y
highlight%28y=1%29


3)
6x+-+10y+=+8........1 .....solve for x
5x+-+6y+=+16..........2
-----------------------------
6x+-+10y+=+8........1
6x+=+10y+%2B+8

x+=+10y%2F6+%2B+8%2F6.........substitute in 2
----------------------------------------------
5%2810y%2F6+%2B+8%2F6%29+-+6y+=+16..........2....solve for y
5%2810y%2B+8%29%2F6+-+6y+=+16

0.833%2810y%2B+8%29+-+6y+=+16
8.33y%2B+6.664+-+6y+=+16
2.33y+=+16-6.664
2.33y+=9.336
y+=9.336%2F2.33
highlight%28y+=4.007%29
now find x
x+=+10y%2F6+%2B+8%2F6
x+=+10%284.007%29%2F6+%2B+8%2F6
x+=+%2840.07%29%2F6+%2B+8%2F6
x+=+6.678+%2B+1.33
highlight%28x+=+8.008%29
6x+-+10y+=+8
4)
-5x+-5y+=+0.....1 .....solve for x
7x+%2B+4y+=+24+...2
-------------------------
-5x+-5y+=+0.....1
-5x%2B5x+-5y+=+0%2B5x
-5y+=+5x
-5y%2F5+=+5x%2F5
x=-y+.................substitute in 2
-------------------------------
7%28-y%29+%2B+4y+=+24+...2..solve for y
-7y+%2B+4y+=+24+
-3y++=+24+
y++=+24%2F-3+
highlight%28y++=+-8%29+

now find x
x=-y+
x=-%28-8%29+
highlight%28x=8%29