1. -x+9y=-5
x-5y=1
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x=1+5y
-(1+5y)+9y=-5
-1-5y+9y=-5
-1+4y=-5
4y=-5-(-1)
4y=-5+1=-4
4y=-4
y=-4/4=-1
So x=1+5y=1+5(-1)=1-5=-4
Answer: x=-4, y=-1. (-4, -1).
2) -7x-y=13
8x+y=-14
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y=-14-8x
-7x-(-14-8x)=13
-7x+14+8x=13
14+x=13
x=13-14=-1
y=-14-8(-1)=-14+8=-6.
Answer: x=-1, y=-6. (-1, -6).
3) x+7y=24
x-9y=-24
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x=24-7y
24-7y-9y=-24
24-16y=-24
16y=24-(-24)=24+24=48
y=48/16=3
x=24-7(3)=24-21=3
Answer: x=3, y=3. (3, 3).
4). 3x+y=-21
x+y=-5
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x=-5-y
3(-5-y)+y=-21
-15-3y+y=-21
-15-2y=-21
2y=-15-(-21)=-15+21=6
y=6/2=3
x=-5-3=-8.
Answer: x=-8, y=3. (-8, 3).
5) 3x+6y=6
9x-12y=18
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Simplify 3x+6y=6 will get you x+2y=2,
x=2-2y,
9(2-2y)-12y=18
18-18y-12y=18
18-30y=18
30y=18-18=0
y=0/30=0
x=2-2(0)=2-0=2
Answer: x=2, y=0. (2, 0).
6) 6x+8y=26
-7x+2y=-19
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-4(-7x+2y)=-4(-19)
28x-8y=76
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6x+8y=26
28x-8y=76
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34x=102
x=102/34=3
6(3)+8y=26
18+8y=26
8y=26-18=8
y=8/8=1
Answer: x=3, y=1. (3, 1)
BONUS:
-5x+5y=-25
3x+2y=10
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Simplify -5x+5y=-25 you will get x-y=5
x=y+5
3(y+5)+2y=10
3y+15+2y=10
5y+15=10
5y=10-15=-5
y=-5/5=-1
x=-1+5=4
Answer: x=4, y=-1. (4, -1).
Answer:
8 (19) or 8 (18 +1)
Step-by-step explanation:
Distributive property means to distribute.
HCF of 144 and 8.
=> 8 is the HCF of 144 and 8
8 (18 + 1)
=> 8 (19)
I'm not 100% sure if I am right, but for number 9 you would pick two points on , let's just say you pick points (0, 1) and (2, -2). Then you would find those points in the table. So in this case the answer would be D. And I'm not really sure how to explain #10 but you basically work out each problem with the graph to see if it makes sense. For example if you try working out problem F it wouldn't make sense since you start of with 10 dollars and earn 2 each day. But on the graph it shows that you are loosing two. Sorry if I didn't explain it right, if you have more questions let me know!
Given:
Number of black marbles = 6
Number of white marbles = 6
Let's determine the least number of marbles that can be chosen to be certain that you have chosen two marble of the same color.
To find the least number of marble to be chosen to be cartain you have chosen two marbles of the same color, we have:
Total number of marbles = 6 + 6 = 12
Number of marbles to ensure at least one black marble is chosen = 6 + 1 = 7
Number of marbles to ensure at least one white marble is chosen = 1 + 6 = 7
Therefore, the least number of marbles that you must choose, without looking , to be certain that you have chosen two marbles of the same color is 7.
ANSWER:
7
