Answer:
<h2>
x = (12-k)/2, y = k, z = (k-6)/4 </h2>
Step-by-step explanation:
Given the system of equation
x + y - 2z = 9 ... 1
3x + y + 2z = 15 ...2
x - 5y + 22z = -27... 3
First let us reduce the system of equation into two with two unknowns.
Subtracting 1 from 3
y-(-5y) + (-2z-22z) = 9-(-27)
y+5y + (-24z) = 9+27
6y-24z = 36 ... 4
Multiplying equation 1 by 3 and subtracting from equation 2
3x + 3y - 6z = 27
3x + y + 2z = 15
On subtracting both;
(3y-y)+(-6z-2z) = 27-15
2y-8z = 12 ... 5
Equating 4 and 5
6y-24z = 36 ... 4
2y-8z = 12 ... 5
Multiplying equation 5 by 3 the equation becomes;
6y-24z = 36 ... 6
6y-24z = 36 ... 7
We can see that equation 6 and 7 are the same;
let y = k
6k - 24z = 36
k - 4z = 6
4z = k-6
z = k-6/4
Substituting y = k and z = k-6/4 into equation 1 to get x
From 1; x + y - 2z = 9 ... 1
x + k -2( k-6/4) = 9
x + k - (k-6)/2 = 9
x = 9+(k-6)/2-k
x = {18+(k-6)-2k}/2
x = (12-k)/2
The solutions to the system of equations are x = (12-k)/2, y = k, z = (k-6)/4 where k is any constant. This shows that the system of equation has infinite solutions.
Answer:
300 miles
Step-by-step explanation:
just do 3 times 4 you get 12 so you do 4 times 75 and you get 300
Answer:
She can make cookies for 4.95 weeks
Step-by-step explanation:
2 x 1 2/3 = 3.333333333
16.5/ 3.333333333 = 4.95
Since Jordan is making two batches of Cookies per week, you need to multiply 2 by the amount of resources needed to bake one batch of cookies. So you multiply 1 and 2/3 by 2 to get the amount of resources neccesary for one week of making cookies. Then, you take the full amount of resources that she has, and divide that by the amount she uses per week, that number will give you the number needed to figure out how many weeks she has to bake cookies.
To figure out the number that is being divided to get the whole number in weeks, you would take the 16.5 cups of flour. The reason why this is, is because that Is the starting number of cups that she has. So here you would need to divide the amount you are taking from it each week. This will result in the amount of weeks that she is able to bake cookies with her flour.
Answer: - 8
Step-by-step explanation:
x/4 - 5 = -7
=> x/4 = -2
=> x = -8
