Answer:
According to the numbers provided, the sequence is:
5, 6, 1, 4, 7, 3, 2
Solution of the two lines intersecting in the graph is answer B
The inequality that represents the graph is that of answer A
Step-by-step explanation:
First problem:
This is the sequence to solve for "x" once the substitution was made;
[tex]3x +2\,(x+3)=11\\3x+2x+6=11\\5x+6=11\\5x=11-6\\5x=5\\x=1\\[/tex]
Now that we know x, we use its value (1) in the substitution equation in order to find "y" and complete the ordered pair:
[tex]y=x+3\\y=1+3\\y=4[/tex]
Then the solution pair (x, y) is: (1, 4)
Therefore, according to the numbers provided in the list of possible steps, the order is:
5, 6, 1, 4, 7, 3, 2
Second problem:
The solution to the system is where the two lines two lines intersect: "the point -1.5 on the x axis. Notice that -1.5 can be written in fraction form as -3/2, this is the x-coordinate of the intersection point. The y-coordinate is y-0 since the point is on the x-axis. Therefore the point is (-3/2, 0) which is given by answer B).
Third problem: The boundary line seems to go through the points: (-4, -10) and (0, -2), so we can calculate the slope via the equation:
[tex]slope=\frac{y_2-y_1}{x_2-x_1} \\slope=\frac{-2-(-10)}{0-(-4)}\\slope=\frac{8}{4}\\slope=2[/tex]
since the line's y-intercept is (0, -2), then the equation of the boundary line in slope-intercept is:
[tex]y=2x-2[/tex]
Since the shaded region includes the boundary line and the zone above it (with y-values larger than or equal to those point in the line), we can say that the inequality that represents this graph is:
[tex]y\geq 2x-2[/tex]
which corresponds to answer A
