This is the set of all points on one side of a line in the coordinate plane. It's can be described as the solution set for a linear inequality in two variables

The solution region of a linear inequalities

Step-by-step explanation:

The solution region of a linear inequalities is the region with coordiates  that satisfy the condition of the linear inequalities solution.

For example:

Find the solution region for x + y > 4

Step 1: Draw the line x + y = 4

An easy way to plot the line is to find the points where the line cut across  the x and y axis.

1.1 To find a point where the line cut across the x axis i.e the point where       y = 0

x + y = 4

x + 0 = 4

Therefore x = 4

The point (x,y) = (4,0) is the point where the line cut across the x axis

1.2 To find a point where the line cut across the y axis i.e the point where       x= 0

x + y = 4

0 + y = 4

Therefore y = 4

The point (x,y) = (0,4) is the point where the line cut across the x axis

Step 2: Find the region that satisfy x + y > 4 i.e the region where the summation of the coordinate is greater than 4

2.1 picking a point to the left of the line e.g (1,1)

x + y =  1+1 = 2

The result 2 does not satisfy the inequalities i.e it is not greater than 4

2.2 picking a point to the right of the line e.g (3,2)

x + y =  3+2 = 5

The result 5  satisfy the inequalities i.e it is  greater than 4

Therefore the region to the right of the line x + y = 4 satisfy x + y > 4

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.