8th Grade Algebra Answer Check
posted by Lily on .
Solve each system of equations, give the solution and state whether there are no solutions or many solutions.
1 )3x + 8y = 1
7x + 4y = 17
Answer: (3,1)
2) 3x + 5y = 7
9x + 2y = 38
Answer: (4,1)
3) 7r + 3s = 13
14r  15s = 16
Answer: (1,2)
4) 2x  7y = 42
4x  14y = 64
Answer: No Solution ??
5) 9x + 12y = 15
3x + 4y = 5
Answer: Identity ??
6) 2 = 4s  3t
2 = 12s  9t
Answer: No Solution ??
7) 3a  6b = 18
4a + 8b = 24
Answer: (6,0)
If I got any of these wrong, can someone please show me the right way to do them?
These I have no idea on how to do them.
8) 4x +8y = 5
5x +10y = 13
9) 13 = 8a  8b
6 = 4a  5b
10) 160 = 2x  10y
120 = 3x  15y
Can anyone show me how to do these ones, I keep trying to solve them, but keep getting the wrong answer?

#8 has no solution, here is why...
1st one times 5
20x + 40y = 25
2nd one times 4
20x + 40y = 52
subtract them
0 = 27 which is false
if it ever happens that the variables disappear and the remaining statement is false, there is no solution.
If the remaining statement would be true, such as in 0 = 0, there would be an infinite number of solutions.
#9.
1st one :
13 = 8a  8b
2nd one times 2
12 = 8a  10b
subtract the first equation minus the new second one
1 = 2b
b = 1/2
back in #1
13 = 8a  4
17 = 8a
a = 17/8
check in original 2nd
LS = 6
RS = 4(17/8)  5(1/2)
= 17/2  5/2
= 12/2 = 6 = LS
#10 is just like #8
see if you finish it yourself 
a times a + b times b =11 and a times b =3 what does a and b equals

two kinds of grouping symbols