Solve this system of inequalities graphically 3-y<6, x>1, y<3
rearrange the equations to ...
y>-3 and
x>1 and
y<3
This means that y is between -3 and 3, x>1
Does that help?
If f (x) - 4x - 3, find the following f (-1)
Sorry, I can not graph this for you.
However
3 - y < 6
Multiply both sides by -1, when you multiply inequality by negative quantity, change direction of arrow
-3 + y > -6
or
y > -3
So everything above the horizontal line y = -3 is in so far.
x>1 so everything above -3 and right of x = 1 is in so far
y <3 so everything between y = -3 and y = +3 and right of vertical line x=1 is in
Mary, use - 1 for x
Since you did not type an equal sign I assume you mean
If f (x) = 4x - 3, find the following f (-1)
f(-1) = 4 *(-1) - 3
= -4 -3
= -7
To solve the system of inequalities graphically, we will plot the corresponding lines and then shade the region where the inequalities are satisfied.
First, let's rewrite the inequalities in slope-intercept form:
1. 3 - y < 6 can be rewritten as y > -3
2. x > 1 remains the same
3. y < 3 remains the same
Now let's plot the lines:
1. For y > -3, draw a dashed line parallel to the x-axis, just below the y = -3 line. Indicate with arrows that the line continues indefinitely in both directions.
2. For x > 1, draw a vertical dashed line passing through x = 1. Indicate with an arrow that the line extends to the right indefinitely.
3. For y < 3, draw a dashed horizontal line passing through y = 3. Indicate with an arrow that the line extends indefinitely to the left.
Now, let's shade the region that satisfies all three inequalities:
- Shade the region above the y = -3 line (since y > -3).
- Shade the region to the right of the x = 1 line (since x > 1).
- Shade the region below the y = 3 line (since y < 3).
The shaded area in the graph represents the solution to the system of inequalities.
Note: Since we have two dashed lines, the boundaries of the shaded region are not included in the solution.