Question 193464
#1. 
x + 2y = 15
x - 2y = -9
-------------note if we add these, we eliminate y, then we can find x easily
2x = 6
x = {{{6/2}}}
x = 3
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Substitute 3 for x in the 1st equation and find y 
3 + 2y = 15
2y = 15 - 3
2y = 12
y = {{{12/2}}}
y = 6
:
Check both solutions in the 2nd equation, substituting for x and y
3 - 2(6) = 12; equality reigns, confirms your solutions
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#2.
 x - y = 0
7x -3y =24
From the 1st equation we can see x = y, substitute y for x in the 2nd equation
7y - 3y = 24
4y = 24
y = {{{24/4}}}
y = 6 and x = 6 also
:
Check in 2nd equation
7(6) - 3(6) = 24
42 - 18 = 24
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#3.
3x - 8y = 10
 x - 4y = 3
:
Here we can multiply the 2nd by 3 and subtract from the 1st eq, eliminate x
3x - 8y = 10
3x -12y = 9
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0x + 4y = 1
y = {{{1/4}}}
:
Substitute 1/4 for y in the 2nd original equation, find x
x - 4(1/4) = 3
x - 1 = 3
x = 4 + 1
x = 4
:
Check solution in the 1st equation:
3(4) - 8(1/4) =  10
12 - 2 = 10; confirms our solution
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#4. 
2x + 3y = -5
3x - y = 20
Use straight substitution here using the 2nd equation
-y = 20 - 3x
Y had to be positive, multiply both sides by -1
y = 3x - 20
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Substitute (3x-20) for y in the 1st equation
2x + 3(3x+20) = -5
2x + 9x - 60
11x = -5 + 60
11x = 55
x = {{{55/11}}}
x = 5 
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we said y = 3x - 20
y = 3(5) - 20
y = 15 - 20
y = -5
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Why don't you check these solutions in both equations