Question
The graph of a system of linear equations is given y=3-1/3x y=2/3x what is the solution of the system
Answers
GPT 3.5
To find the solution of the system of linear equations, we need to find the point where the two lines intersect.
First, let's rewrite the equations in slope-intercept form (y = mx + b) to make it easier to graph:
1. y = 3 - (1/3)x
2. y = (2/3)x
Now, let's plot the two equations on a graph:
The first equation has a y-intercept of 3 and a slope of -1/3. It will intersect the y-axis at (0,3) and have a negative slope.
The second equation has a y-intercept of 0 and a slope of 2/3. It passes through the origin (0,0) and has a positive slope.
When we plot both equations, the lines will intersect at a point. This point is the solution to the system of linear equations.
Upon graphing the equations, we can see that the lines intersect at the point (3, 2). Therefore, the solution to the system of linear equations is x = 3 and y = 2.
First, let's rewrite the equations in slope-intercept form (y = mx + b) to make it easier to graph:
1. y = 3 - (1/3)x
2. y = (2/3)x
Now, let's plot the two equations on a graph:
The first equation has a y-intercept of 3 and a slope of -1/3. It will intersect the y-axis at (0,3) and have a negative slope.
The second equation has a y-intercept of 0 and a slope of 2/3. It passes through the origin (0,0) and has a positive slope.
When we plot both equations, the lines will intersect at a point. This point is the solution to the system of linear equations.
Upon graphing the equations, we can see that the lines intersect at the point (3, 2). Therefore, the solution to the system of linear equations is x = 3 and y = 2.