Answer:
Infinite solution
Step-by-step explanation:
Let, number of Capulet family = x and number of Montague family = y.
Since, last year, each Capulet wrote 4 essays and each Montague wrote 6 essays.
Moreover, total essays wrote last year are 100.
So, we get, 4x + 6y = 100.
Again, this year, each Capulet wrote 8 essays and each Montague wrote 12 essays.
Moreover, total essays wrote this year are 200.
So, we get, 8x + 12y = 200.
Thus, the system of equations is given by,
4x + 6y = 100.
8x + 12y = 200.
Dividing first equation by 2 and second equation by 4, we get the equation,
2x + 3y = 50.
Since, there is only one equation and two variables i.e. x and y.
There can be infinite number of possibilities for the values of x and y.
There will be infinitely many solutions for the system of linear equations for the number of members of The Capulet and Montague family's love of writing.
It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
If in the linear equation one variable is present then the equation is known as the linear equation in one variable.
Let's suppose the number of members in the Capulet is x and in Montague is y.
From the problem we can frame two linear equations:
4x + 6y = 100 ...(1)
8x + 12y = 200 ...(2)
Divide by 2 on the equation (2)
4x + 6y = 100 ...(3)
Equations (1) and (2) have the same coefficient of x and y
It means there will be infinitely many solutions for the system of linear equations.
Thus, there will be infinitely many solutions for the system of linear equations for the number of members of The Capulet and Montague family's love of writing.
Learn more about the linear equation here:
brainly.com/question/11897796
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