Substitution: x+3y=-4, so x=-4-3y and 3(-4-3y)-7y=36, -12-9y-7y=36, -9y-7y=48, -16y=48, y=-3. and x=x+3(-3)=-4, x-9=-4, x=5. Thus, the ordered pair is (5, -3).
Elimination: We can also show this by elimination: multiply the first equation by 3, which yields, 3x+9y=-12 and 3x-7y=36. Subtract, 16y=-48, y=-3. Plugging the value of y back in to find the value of x, we get x+3(-3)=-4, x-9=-4, x=5. Thus, the ordered pair is (5, -3).
Okay, again, let's try to solve here for the solution of the system.
Here, we can use elimination, or if you want to try; substituion.
We have x-y=3 and 7x-y=-3. If we add subtract both equations, the y's will cancel out, so that's good!
Therefore, we get x-7x=3-(-3), which is -6x=6 and x=-1.
Plugging the value of x for the value of y, we attain -1-y=3, -y=4, y=-4. So, it is a solution to the system! (B) works.
We can try plugging in this system to see if this works for both equations. Doing so, we get -1-(-4)=3, -1+4=3, True!, (C)
And, for the second equation, 7(-1)-(-4)=-3, -7+3=-3, Yes! So, (E) works!
Thus, the answer is (B), (C), and, (E).
First, let's try to solve the system of equations; 2x+3y=12, 4x+2y=10.
If we find the LCM of 2 and 4, which is 4, we can multiply the entire first equation by 2.
Therefore, 4x+6y=24 and 4x+2y=10.
In this process of elimination, we can subtract the first equation from the second equation.
Doing so, we get 4y=14, and y=14/4 or y=7/2 (3.5).
We just plug the value of y in the equations, to solve for the value of x.
Again, doing so, we get 2x+3(3.5)=12, 2x+10.5=12, 2x=1.5, x=0.75.
Now that we have solved for the value of x and y, we can put in parenthesis.
So, we have (0.75, 3.5), which rounds to (1, 4) or the third option.
Hmm, not that good at these type of problems, but I'll give a shot at it!
There are 3! or 6 ways to choose the three couples to sit.
So, 6*8=48 ways to sit three couples, and 8 ways to choose the order the couples sit in.
Finally, there are a total of 6!=720 ways the six individual people can sit.
Thus, 1/15 is our answer..simplified from 48/720.