Write the system of linear inequalities to represent each graph

Linear inequalities are similar to the slope-intercept form, which is:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0) or (0,y)

The difference is that the sign is not an equal sign, so instead of =, you use < , > , ≤ , ≥.

When the sign is ≤ or ≥ ("less/greater than or equal to") the line is a solid line.

When the sign is < or >, the line is a dotted line.

When y is > (greater than), the shaded area is above the line.

When y is < (less than), the shaded area is below the line.

BLUE LINE:

Since the line is a solid line, and the shaded area is above the line, the sign is ≥.

y ≥ mx + b

When x = 0, y is 2, so the y-intercept is 2.

y ≥ mx + 2

To find the slope, you can use the slope formula and find and plug in two points. Or you can use this:

Rise is the number of units you go up(+) or down(-)

Run is the number of units you go to the right

If you look at the blue line, from each point, you go up 1 unit, and to the right 2 units. So the slope is

GREEN LINE:

The line is a solid line, and the shaded area is below the line, so the sign is ≤.

y ≤ mx + b

When x = 0, y is -1, so the y-intercept is -1

y ≤ mx - 1

If you look at the green line, from each point, you go up 1 unit, and to the right 3 units. So the slope is .

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3