Solve the system by graphing. Tell whether the system has one​ solution, infinitely many​ solutions, or no solution.

Question

2x + y = 4

2y = 12 - 4x

Answer 1

To solve the system by graphing, we need to plot the equations on a coordinate plane and see where they intersect, if at all.

Let's start with the first equation:
2x + y = 4

To graph this equation, we can rearrange it to solve for y:
y = -2x + 4

We can now plot this equation on a graph:

Next, let's move on to the second equation:
2y = 12 - 4x

We can rearrange this equation to solve for y as well:
y = -2x + 6

Plotting this equation on the same graph:

Now we can see that the two lines intersect at the point (2, 0). This means that the system has one solution. Therefore, the solution to the system of equations is x = 2, y = 0.

Answer 2

Solve the system by graphing. Tell whether the system has one​ solution, infinitely many​ solutions, or no solution.

2x + y = 3

3y = 18 - 6x

Answer 3

To solve the system by graphing, we need to plot the equations on a coordinate plane and see where they intersect, if at all.

Let's start with the first equation:
2x + y = 3

To graph this equation, we can rearrange it to solve for y:
y = -2x + 3

We can now plot this equation on a graph:

Next, let's move on to the second equation:
3y = 18 - 6x

We can rearrange this equation to solve for y as well:
y = -2x + 6

Plotting this equation on the same graph:

Now we can see that the two lines are parallel. This means that they will never intersect, and the system has no solution. Therefore, the system of equations has no solution.