Question

Samuel and Hayden solved the system of equations –6x – 6y = –6 and 7x + 7y = 7. Samuel says there are infinitely many solutions, but Hayden says the solution is (1,1). Explain who is correct.

Answer 1

Answer:

Samuel is correct i.e  there are infinitely many solutions

Step-by-step explanation:

Given that Samuel and Hayden solved the system of equations –6x – 6y = –6 and 7x + 7y = 7. we have to find that whether the system of equations has infinitely many solutions or not.

A system of linear equations has infinite solutions if the graphs are the exact same line i.e the the equations are equivalent.

The first equation:  –6x – 6y = –6 ⇒ x+y=1 ⇒ y=-x+1

∴ the slope of its line is -1 and the y-intercept is 1

The second equation:  7x + 7y = 7 ⇒  x+y=1 ⇒ y=-x+1

∴ the slope of its line is -1 and the y-intercept is 1.

Here, we get the equation which has the same slope and y-intercept as that of the first equation.

In other words, the two equations are represented by the same line. This implies that the lines intersect infinitely many times, or that the system has infinitely many solutions.

Hence, Samuel is correct.

Answer 2

Answer:

Step-by-step explanation:

Sample Response: The first step in solving this system is to multiply the first equation by 7 and the second equation by 6. When you add the equations, both variables are eliminated and you are left with 0 = 0, which is a true statement. That means there are infinitely many solutions and Samuel is correct.