Which is the best description of the equivalency of the two expressions?

They are equivalent expression because when x = 2, the expressions have the same value.

Step-by-step explanation:

Equivalent expressions are identified when the value of the variable can be substituted in each equation and the same result is found.  So, even though the expression may look different, when you put the same number in for the variable, you will get the same value.  You can also 'simplify' your expressions by combining like terms:

Expression 1:  5x² - 2x + 6x  - 4 + 3 = 5x² + 4x - 1

Expression 2:  6x² - x² - 6x + 10x + 6 - 7 = 5x² + 4x -1

Since both expressions are the same after simplifying, they will produce the same value when x = 2, so they are equivalent.  

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be