Solve the following system of equations: 3x − 2y = 6 6x − 4y = 12 (0, 0) (6, 12) Infinitely many solutions No solutions
2 answers:
<u>Answer:</u>
The correct answer option is: infinitely many solutions.
<u>Step-by-step explanation:</u>
We are given the following system of equations:
--- (1)
--- (2)
Dividing equation (2) by 2 to get:
--- (3)
As the equation (3) is same as the equation (1), therefore the system will have infinitely many solutions.
You might be interested in
The correct answer is c. 2 hours
Explanation:
The graphic shows the relationship between the distance Erin covers by running and the time this requires. Additionally, to know the specific time that takes for Erin to run a specific distance or vice versa it is necessary to observe at which point the two variables intersect in the line of the graph.
According to this, Erin runs 25 miles (y-axis) in 2.5 hours (x-axis), which you can know because in the line shown by the graph the distance 25 miles that is in the middle of 20 and 30 miles intersects with 2.5 hours or the middle between 2 and 3. Additionally, this number can be expressed as 2 and a half hours, 2.5 or even 2 hours because the fraction represents half. This makes option C the answer.
Answer: 90
Step-by-step explanation:
The formula for calculating the nth term of a sequence is given as :
= a + ( n - d )
Where a is the first term
d is the common difference and
n is the number of terms
This means that the 4th term of an arithmetic sequence will have the formula :
= a + 3d
And the 4th term has been given to be , 12 ,substituting into the formula we have
12 = a + 3d .............................. equation 1
Also substituting for the 8th term , we have
36 = a + 7d .............................. equation 2
Combining the two equations , we have
a + 3d = 12 ................... equation 1
a + 7d = 36 ------------ equation 2
Solving the system of linear equation by substitution method , make a the subject of formula from equation 1 , that is
a = 12 - 3d ................... equation 3
substitute a = 12 - 3d into equation 2 , equation 2 then becomes
12 - 3d + 7d = 36
12 + 4d = 36
subtract 12 from both sides
4d = 36 - 12
4d = 24
divide through by 4
d = 6
substitute d = 6 into equation 3 to find the value of a, we have
a = 12 - 3d
a = 12 - 3 ( 6)
a = 12 - 18
a = -6
Therefore , the 17th term of the sequence will be :
= a + 16d
= -6 + 16 (6)
= -6 + 96
= 90
Therefore : the 17th term of the sequence is 90