find the solution to the system of equations by graphing. y=3x-1 -3x+y=-2
(4,11)
(1,1)
no solution
infinitely many solutions
AAAaannndd the bot gets it wrong yet again!
No solutions. The two equations are
y=3x-1
y=3x-2
which are parallel lines
Apologies for the mistake. You are correct. The two equations are parallel lines with the same slope (3) but different y-intercepts (-1 and -2). Therefore, there is no intersection point, meaning there are no solutions to the system of equations.
To find the solution to the system of equations by graphing, we need to plot the equations on a graph and see where they intersect.
The first equation is y = 3x - 1. Let's plot it:
For x = 0, y = 3(0) - 1 = -1. So we have the point (0, -1).
For x = 1, y = 3(1) - 1 = 2. So we have the point (1, 2).
For x = 2, y = 3(2) - 1 = 5. So we have the point (2, 5).
Plotting these points and drawing a line through them, we get:
Now let's plot the second equation, -3x + y = -2.
For x = 0, -3(0) + y = -2 => y = -2. So we have the point (0, -2).
For x = 1, -3(1) + y = -2 => y = 1. So we have the point (1, 1).
For x = 2, -3(2) + y = -2 => y = 4. So we have the point (2, 4).
Plotting these points and drawing a line through them, we get:
Now we can see that the lines intersect at the point (1, 1).
Therefore, the solution to the system of equations by graphing is (1, 1).
To solve the system of equations by graphing, we can plot the equations on a coordinate plane and find the intersection point(s).
Plotting the first equation, y = 3x - 1, we can see that it has a slope of 3 and a y-intercept of -1.
Plotting the second equation, -3x + y = -2, we can rearrange it to y = 3x - 2. It also has a slope of 3 but a y-intercept of -2.
The two equations have the same slope (3), but different y-intercepts. Therefore, the lines are not parallel, and they intersect at a single point.
From graphing, it can be observed that the lines intersect at the point (1, 1).
Thus, the solution to the system of equations is (1, 1).