Solve each system of inequalities

Question

Solve each system of inequalities

1)y <2x+4

2x-y <=4

 

2)y>1/4×

Y<=-x+4

Answer 1

I hope that this information that I used in my classes will help you:

 

GRAPHING LINES AND LINEAR INEQUALITIES


Given a linear equation, you can “solve for y”. This may involve transposing terms. Even when you have an inequality, you can still “solve for y”.

You have your equation or inequality in the form or or the like. Now you know the y-intercept (it’s “b”) and your line (or boundary line) passes through that point on the y-axis.

To draw the line, you need to find the x-intercept. Use and set y = 0. Now solve for x; this value is the x-intercept. Find that point on the x-axis, and draw your line connecting these two axis intercepts.

For an inequality’s boundary line, draw it as a dashed line if the inequality does not include the = case.

When you deal with an inequality, you shade the half-plane ABOVE the boundary line, if the inequality was of the y > (or ) type; otherwise BELOW for the y < (or ) type.


Note: Using this method means that there is no need for a ‘test point’ as taught in the textbook.

When an inequality is of the form x > 5, the boundary line is vertical, and the shaded half-plane is to the right of the dashed vertical line passing through 5 on the x-axis. For x < -2, the shading is to the left of the dashed vertical line passing through -2 on the x-axis.