firat we need to get two equation with two varibles let us work on x,y
so adding the first and last one will yield
now we since we used the first and third we need to use the second to get a correct system.let us multiply the third by 2 then add the second and third
now we have two equation with the variables x and y
you can solve it algebraically but you can see that the only solution possible is y=0 and x=-1 we have the values for x and y let us choose one of the three main equation and substitute to get z let us pick the first equation 5x-2y+z=-1-->5(-1)-2(0)+z=-1---->-5+z=-1-------->z=4
to make sure the system works let us check by substituting into the three equations
the first one will be 5x-2y+z=-1--->5(-1)-2(0)+4=-1---->-5+4=-1--->-1=-1 first equation holds
the second equation 3x+y+2z=6---->2(-1)+0+2(4)=6--->-2+8=-6--->-6=-6 second equation holds
the third equation x-3y-z=-5----->-1-3(0)-4=-5---->-1-4=-5--->-5=-5
our third equation also holds which makes our solution correct
x=-1,y=0,z=4
Answer:
x - y = 3(x + 2)
- x - y = 3x + 6 is the simplified answer and is also correct
Step-by-step explanation:
The difference of x and y is the same as 3 times the sum of x and 2
x - y = 3(x + 2)
x - y = 3x + 6
Answer:
72 guests
Step-by-step explanation:
We can add up the numbers of bottles per guest, then use that total to find the number of guests from the number of bottles.
<h3>Setup</h3>
Let g represent the number of guests at the party. Then there are ...
- g/3 bottles of coke
- g/6 bottles of sprite
- g/4 bottles of lift
The total number of bottles is ...
g(1/3 +1/6 +1/4) = 54
<h3>Solution</h3>
Multiplying by the inverse of the coefficient of g, we find its value to be ...
g(4/12 +2/12 +3/12) = g(9/12) = 54
g = 54(12/9) = 72
There are 72 guests at the party.
1. There are 2 dogs to every 1 cat.
2. There are 20 students for every 1 teacher.
3. There are 4 sugar cones to every 7 waffle cones.
