Solve the system of inequalities by graphin
y < 3x+3
3x-y ≤ 4
Use the graphing tool to graph the system.
To solve the system of inequalities, we will graph each inequality on the coordinate plane and shade the regions that satisfy all the given inequalities.
Let's start by graphing the first inequality: y < 3x+3
To graph this inequality, we'll first draw the line y = 3x+3 (with a dashed line since it's a strict inequality). This line has a slope of 3 and a y-intercept of 3, so it passes through the point (0,3) and goes up 3 units for every 1 unit to the right.
Next, since the inequality is y < 3x+3, we shade the region under the line y = 3x+3.
Now let's graph the second inequality: 3x-y ≤ 4
To graph this inequality, we'll first draw the line 3x-y = 4 (with a solid line since it's a non-strict inequality). This line can be rewritten as y = 3x - 4. It has a slope of 3 and a y-intercept of -4, so it passes through the point (0,-4) and goes up 3 units for every 1 unit to the right.
Next, since the inequality is 3x-y ≤ 4, we shade the region below the line 3x-y = 4.
The shaded region that satisfies both inequalities is the overlap of the shaded regions under y = 3x+3 and below 3x-y = 4.
Here is the graph of the system of inequalities:
{{{ graph( 500, 500, -10, 10, -10, 10, y<3x+3, 3x-y<=4) }}}