Solve this linear equations: x + y + z = 34 1x + 10y + 5z = 100
Answers
Answer
To solve this system of linear equations, we can use the method of substitution.
First, let's solve the first equation for x:
x = 34 - y - z
Now, we substitute this value of x into the second equation:
1(34 - y - z) + 10y + 5z = 100
34 - y - z + 10y + 5z = 100
34 + 9y + 4z = 100
Next, we simplify the second equation:
9y + 4z = 100 - 34
9y + 4z = 66
We can rewrite this equation as:
9y = 66 - 4z
y = (66 - 4z) / 9
Now, we substitute this value of y back into the first equation:
x + (66 - 4z) / 9 + z = 34
Multiplying through by 9 to eliminate the fraction:
9x + 66 - 4z + 9z = 306
9x + 5z = 240
Now we have a system of two equations in two variables:
9x + 5z = 240
9y + 4z = 66
We can solve this using the method of substitution or elimination. Let's use the method of elimination:
Multiplying the first equation by 4 and the second equation by 5, we get:
36x + 20z = 960
45y + 20z = 330
Subtracting the second equation from the first, we eliminate z:
36x - 45y = 630
We can simplify this equation by dividing through by 9:
4x - 5y = 70
Now, let's solve the new system of equations:
4x - 5y = 70
9y + 4z = 66
We can multiply the first equation by 9 and the second equation by 4 to eliminate x:
36x - 45y = 630
36y + 16z = 264
Now, subtracting the first equation from the second, we eliminate y:
36y + 16z - 36x + 45y = 264 - 630
81y + 16z = -366
Dividing through by 3, we get:
27y + 16z = -122
Now, we have a system of two equations in two variables:
4x - 5y = 70
27y + 16z = -122
We can solve this system using the method of substitution or elimination.
Related Questions
Write an equation for the function that includes the points (-2,3) and (-1,9)
Can someone answer this question please?
Ozzie is 6 years older than McKenzie. Theo is Ozzie's dad and is 3 times older than McKenzie. Ozzie is 8 years old. How old is Theo?
A standard deck of cards has 52 members consisting of 4 suits each with 13 members (2, 3, …, 10, j, q, k, a). five cards are dealt from the randomly mixed deck. what is the probability that all cards are the same suit
Answers
15 students
2 students must be chosen.
No repetition, no order
This is a combinations problem. We use this formula: n! / (n-r)!(r!)
n = 15 ; r = 2
15! / (15-2)!(r!) ⇒ 15! / 13! * 2! = 105
Using the combination formula, it is found that the students can be selected in 105 ways.
The order in which the students are selected is not important, hence the combination formula is used to solve this question.
What is the combination formula?
The number of possible combinations of x elements from a set of n elements is given by:
In this problem, two students are selected from a set of 15, hence the number of different orders is given by:
More can be learned about the combination formula at brainly.com/question/25821700
#SPJ5
Answers
Answer:
A=30,32,44,48
B=22,34
intersect=26
numbers going outside is 24,28,36,38,40,42,46
b) 1/14
Step-by-step explanation:
a)The numbers that will go into the A bracket will be 30,32,44 and 48. The numbers that will go into the B bracket will be 22 and 34. The number that will go into the intersect will only be 26. And finally the numbers going on the outside of the venn diagram will be 24,28,36,38,40,42,46.
b)The answer will be 1/14
Answers
Answer:
They cannot afford the monitors
Step-by-step explanation:
Given that the cost of a monitor is $89
and the school is willing to buy up to 200 monitors
We can calculate the total cost of all the 200 monitors as
200*89= $17,800
Given that the school only has $ 15,000 to spend on the monitor
they cannot afford the amount as they still have a deficit of $2,800
Answers
Answer:
[0,12]
Step-by-step explanation:
B. Figure B
C. Figure C
D. Figure D
Answers
Answer:
A. Figure A
Step-by-step explanation:
The protractor on the top left has an arrow halfway inbetween 50° and 60, making the angle 55°.
Therefore, the answer is Figure A.
Answers
8 = a + bi
Answer: a=8, b=0