Solve the following system of inequalities by graphing.

y<2x+3
y≤-4x+5
y<2x+3
y≤-4x+5
Step 1:
Write a linear equation for the inequality y < 2 x + 3
The related equation is y = 2 x + 3
Step 2 : Find the x- and the y-intercepts for this equation
For finding x-intercept plug in y = 0 in y = 2 x + 3 to get x = \frac{-3}{2} = 1.5
For finding the y-intercept plug in x = 0 in y = 2 x + 3 to get y = 3
Step 3 : Plot the x- and the y-intercepts on the graph
Plot (-1.5,0) and (0,3) on the graph and join these points to get a straight line
Step 4:
Write a linear equation for the inequality y \leq -4 x + 5
The related equation is y = -4 x + 5
Step 5 : Find the x- and the y-intercepts for this equation
For finding x-intercept plug in y = 0 in y = -4 x + 5 to get x = - 1.25
For finding the y-intercept plug in x = 0 in y = -4 x + 5 to get y = 5
Step 6 : Plot the x- and the y-intercepts on the graph
Plot (-1.25,0) and (0,5) on the graph and join these points to get a straight line
Step 7: Shade the inequalities