The first set:
3x + 2y = 2 ---1)
5x + 4y = 6 ---2)
From 1), multiply all by 2, 6x + 4y = 4 ---3)
3) - 2),
6x + 4y - (5x + 4y) = 6 - 4
6x + 4y - 5x - 4y = 2
x = 2
Sub in x = 2 into 1),
3(2) + 2y = 2
2y = -4
y = -2
(2 , -2)
The second set:
3x + 2y = 2 ---1)
11x + 8y = 10 ---2)
From 1), multiply all by 4, 12x + 8y = 8 ---3)
3) - 2),
12x + 8y - (11x + 8y) = 8 - 10
12x + 8y - 11x - 8y = -2
x = -2
From this x value alone, we can tell that these two linear systems do NOT have the same solution as they meet at different coordinates.
Hope this helped! Ask me if there's any working from here that you don't understand! :)
If there are 150 total instruments in said Orchestra, we'll need to divide that number in half.
75, simple enough. Now we know that half of 150 is 75.
Start by writing your problem like this: 150= 75w+37.5b
That equation is all I can think of, because 37.5 is half of 75, which means that's roughly the number you're looking for. Sorry if this doesn't help much<span />
Answer:
6/10
Step-by-step explanation:
multiply 3/5 by any whole number ratio equal to 1 to obtain an equivalent fraction.
(2/2)*(3/5) = 6/10
or (3/3)*(2/5) = 9/15
etc.
Answer:
Step-by-step explanation:
Rearrange the terms and take out a common factor of 4
4(8x^2 + 2x + 1)
I think this is as far down as you want to take it. It gives an imaginary root which you may not be familiar with.
Answer:
- 35 5-lb weights
- 25 3-lb weights
Step-by-step explanation:
Let t and f represent the numbers of three- and five-pound weights. The problem statement tells us ...
f + t = 60
f - t = 10
Adding these two equations, we get ...
(f +t) +(f -t) = (60) +(10)
2f = 70 . . . . . eliminate parentheses
f = 35 . . . . . . divide by 2
She has 35 5-lb weights, and 25 3-lb weights.
