the problem is to graph
3x - y < 2
x + y > 2
my solution is y = 3x - 2, y = -1x + 2
I,m lost at where my lines ar drawn. In y = 3x - 2 (y line is 3)
and y = -1x +2 (y line is -1)
or am I totaly lost.
After continued effort I beleive
1st equation
m = 3 and y-intercept is -2
2nd question
m = -1 and y- intercept is 2
However my graph shows 2 parallel lines shading becomes an issue or am I still lost
To graph the system of inequalities:
1. Start by graphing the first inequality, 3x - y < 2.
First, rewrite the inequality as an equation by replacing the inequality sign with an equals sign: 3x - y = 2.
To graph this equation, find the x and y-intercepts:
- For x-intercept, let y = 0, and solve for x: 3x - 0 = 2, which gives x = 2/3.
- For y-intercept, let x = 0, and solve for y: 3(0) - y = 2, which gives y = -2.
Plot these two points on a graph and draw a line passing through them.
2. Graph the second inequality, x + y > 2.
Rewrite the inequality as x + y = 2.
For x-intercept, let y = 0, and solve for x: x + 0 = 2, which gives x = 2.
For y-intercept, let x = 0, and solve for y: 0 + y = 2, which gives y = 2.
Plot these two points on the same graph and draw a line passing through them.
Now, looking at the two lines you drew on the graph, determine which region represents the solution to the system of inequalities.
For the first inequality, 3x - y < 2, choose a test point not on the line (0, 0 is a convenient choice). Substitute this point into the inequality:
3(0) - 0 < 2
0 < 2
Since the test point satisfies the inequality, shade the region below the line.
For the second inequality, x + y > 2, use another test point not on the line (such as (0, 0)):
0 + 0 > 2
0 > 2
Since the test point does not satisfy the inequality, shade the region above the line.
The shaded regions where the two shaded areas overlap represent the solution to the system of inequalities.
If the lines appear parallel and shading becomes an issue, you might have made an error while graphing or in the equations themselves. Review the steps and check for any mistakes made along the way.