What is the common difference for this arithmetic sequence?
2 answers:
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Answer:
Part 1:
The solution set of the system of equations is x = 1, y = 1
Part 2:
The solution set is x = 1, y = 1
Part 3:
The similarity of the system of equations in Parts 1 and 2 is that they have the same solution set
The difference of the system of equations in Parts 1 and 2 is that they are arranged differently
Step-by-step explanation:
Part 1:
The system of equation is given as follows;
2·x + y = 3...(1)
x = 2·y - 1...(2)
The above system of equations can be written in terms of the variable, y, as follows;
For equation (1), we have;
y = 3 - 2·x
For equation (2), we have;
y = (x + 1)/2
From the attached graph created with Microsoft Excel, we have;
The solution set (the point of intersection) of the system of equations is x = 1, y = 1
To accurately find the common solution, we have;
(x + 1)/2 = 3 - 2·x
x + 1 = 2·(3 - 2·x) = 6 - 4·x
x + 1 = 6 - 4·x
x + 4·x = 6 - 1
5·x = 5
x = 5/5 = 1
x = 1
Therefore, y = 3 - 2·x = 3 - 2× 1 = 1, at the common solution
Part 2:
y = -2x + 3
x - 2y = -1
∴ x = 2y -1
y = -2(2y -1) + 3
y = -4y + 2 + 3
5y = 5
y = 1
x = 2y - 1 = 2 - 1 = 1
x = 1
The solution set is x = 1, y = 1
Part 3
The system of equations are similar in terms of their solution
The system of equations are different in terms of their arrangement
