Adding any two positive numbers will result in another positive number.
For example:
7+3 = 10
The values 7, 3 and 10 are positive.
It is impossible to add 2 positive numbers to get a negative number.
Answer:
The three consecutive integers are:
8, 9, 10
Step-by-step explanation:
Given:
There are three consecutive integers.
Three times the smallest is 14 more than the largest.
To find the three integers.
Solution:
Since the integers are consecutive , so each have a common difference of 1.
For example : -3,-2,-1
Let the integers be =
Three times the smallest is 14 more than the largest can be given as:
Simplifying and solving for .
Subtracting both sides by
Dividing both sides by 2.
∴
Smallest integer = 8
Next integer = 9
Largest integer = 10
Answer:
D {50, 150}
Step-by-step explanation:
Hope this solve your answer
Step One
Add the first and third
-2x + 2y + 3z = 0
<u>2x + 3y + 3z = 5</u>
5y + 6z = 5
Step Two
Add the second and third together.
- 2x - y + z = -3
<u>2x + 3y + 3z = 5</u>
2y + 4z = 2 Divide this result by 2
y + 2z = 1 multiply this result by 5
5y + 10z = 5
Step three
Subtract the result of step 2 from the result of step one
5y + 10z = 5
<u>5y + 6z = 5 </u> Subtract
4z = 0
z = 0
Step Four
Solve for y
5y + 6z = 5 But z = 0
5y = 5
y = 1
Step Four
Solve for x . Use equation 3 in the givens.
2x + 3y + 3z = 5
2x + 3*1) + 3*0 = 5
2x = 5 - 3
2x = 2
x = 1
Answer
x = 1
y = 1
z =0 This has been checked and found to be correct.
Problem 2
Substitution is not the best way to do this. Divide the last equation by 2 and add it to the first one.
Step One
divide equation 3 by 2.
x + z = 2
Step Two
Add step one to equation 1
-x - y - z = - 8
<u>x + z = 2</u>
- y = - 6
y = 6
Step Three
Put this result into equation 1.
-x - 6 - z = - 8
-x - z = - 2
x + z = 2 Multiply this equation by 4
4x + 4z = 8
Step four
Put y = 7 into the second equation.
-4x + 4y + 5z = 7
-4x + 4*6 + 5z = 7
-4x + 24 + 5z = 7
-4x +5z = -17
Step 5
Add the results from Step 3 and Step 4 together.
-4x + 5z = - 17
4x + 4z = 8
9z = - 9
z = - 1
Step 6
Find x
-x - y - z = - 8
-x -6 + 1 =- 8
-x - 5 = - 8
-x = - 3
x = 3
Answers
x = 3
y = 6
z = -1 verified to be correct.