Part 1 Solve the system by graphing. Tell whether the system has one​ solution, infinitely many​ solutions, or no solution. y - 3x = 2 6y = 18x + 12

Answer 1

To solve the system by graphing, we will graph each equation on the same coordinate plane and identify the point where the two lines intersect.

First, we'll graph the equation y - 3x = 2. To do this, let's rewrite the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

The equation y - 3x = 2 can be rewritten as:
y = 3x + 2

Now, we can graph the equation y = 3x + 2. Here's the graph:

{{{ graph( 300, 200, -5, 5, -5, 10, 3x + 2) }}}

Next, let's graph the equation 6y = 18x + 12. We'll also rewrite this equation in slope-intercept form:

6y = 18x + 12
y = 3x + 2

This equation is the same as the previous one, y = 3x + 2. Hence, the two equations represent the same line. This means that the system has infinitely many solutions since all the points on the line are solutions.