Question

Graph the following system of equations.

x + 2y = 2
3x+6y= 12
What is the solution to the system?
There is no solution.
There is one unique solution, (0, 1).
There is one unique solution, (2, 1).
There are infinitely many solutions.

Answer 1

Hello!

`x + 2y = 2\\\\\boxed{x = 2 - 2y}`

`3x + 6y = 12\\\\(3x)/(3) + (6y)/(3) = (12)/(3) \\\\x + 2y = 4\\\\\boxed{x = 4 - 2y}`

`2 - 2y = 4 - 2y\\\\-2y + 2y = 4 - 2\\\\\boxed{0 = 2}`

There are no solution

Answer 2

Option: A

Explanation:

To determine the solution to the system of equations, let's first analyze the equations.

The given system of equations is:

1) x + 2y = 2

2) 3x + 6y = 12

To graph this system of equations, we can convert each equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

For equation 1:

x + 2y = 2

2y = -x + 2

y = (-1/2)x + 1

For equation 2:

3x + 6y = 12

6y = -3x + 12

y = (-1/2)x + 2

Now, let's plot these equations on a graph:

The first equation, y = (-1/2)x + 1, has a slope of -1/2 and a y-intercept of 1. This means it will have a negative slope and pass through the point (0, 1).

The second equation, y = (-1/2)x + 2, also has a slope of -1/2 but passes through the point (0, 2).

When we graph these equations, we see that they represent two parallel lines. Parallel lines have the same slope but different y-intercepts, so they will never intersect.

Since the lines do not intersect, there is no solution to the system of equations. Therefore, the correct option is: There is no solution.