SOLUTION: solve each linear system using elimintion a) 4x+5y =14 2x-3y= -2 solve using substitution a) 3a+b-4=0 2a-10=3b b) 3p-6q =0 4p+q=3 i keep trying and when i che

Question 839718: solve each linear system using elimintion
a) 4x+5y =14
2x-3y= -2
solve using substitution
a) 3a+b-4=0
2a-10=3b
b) 3p-6q =0
4p+q=3 i keep trying and when i check its always wrong :(

Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
a) 4x+5y =14
2x-3y= -2
multiply the top equation by 3 and the bottom by 5
12x+15y=42
10x-15y=-10
add them together
22x = 32
x = 32/22
x = 16/11
substitute 16/11 in 2x-3y=-2
2(16/11) -3y = -2
32/11 -3y = -2
add -32/11 to each side
-3y = -2 -32/11
-3y = -22/11 -32/11
-3y = -54/11
y = 18/11
check http://www.wolframalpha.com/input/?i=4x%2B5y+%3D14+%2C+2x-3y%3D+-2
----------------
3a+b-4=0
2a-10=3b
Let's use the first equation to solve for b
3a+b-4= 0
add -3a+4 to each side
b = -3a+4
substitute -3a+4 for b in 2a-10=3b
2a-10=3(-3a+4)
2a-10=-9a+12
add 9a to each side
11a -10=12
add 10 to each side
11a = 22
a = 2
substitute 2 for a in b = -3a+4
b=-3(2)+4
b=-6+4
b=-2
----------------------
3p-6q =0
4p+q=3
Using the second equation solve for q
add -4p to each side
q = 3 -4p
substitute 3-4p for q in 3p-6q =0
3p-6(3-4p) =0
3p-18+24p = 0
27p -18 = 0
add 18 to each side
27p = 18
divide by 27
p = 18/27
p = 2/3
substitute 2/3 for p in q = 3 -4p
q = 3 -4(2/3)
q = 3 -8/3
q = 9/3 -8/3
q = 1/3
These are pretty difficult for this type of problem.
Check out www.wolframalpha.com
Put a comma between equations.
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