A consistent system of equations has at least one solution.
A consistent system is considered to be an independent system if it has a single solution, such as the example we just explored. The two lines have different slopes and intersect at one point in the plane.
A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line. Every point on the line represents a coordinate pair that satisfies the system. Thus, there are an infinite number of solutions.
Another type of system of linear equations is an inconsistent system, which is one in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no points common to both lines; hence, there is no solution to the system.
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Answer:
(0,-7)
Step-by-step explanation:
the y-intercept is found when the x-value is equal to 0. In this case, we are finding a coordinate pair. First, plug in 0 for x.
7+y=4.3(0)
simplify
7+y=0
subtract 7 from both sides
y=-7
Make it an ordered pair,
(0,-7)
Given the table showing the distance Randy drove on one day of her vacation as follows:
![\begin{tabular} {|c|c|c|c|c|c|} Time (h)&1&2&3&4&5\\[1ex] Distance (mi)&55&110&165&220&275 \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7Cc%7Cc%7Cc%7Cc%7C%7D%0ATime%20%28h%29%261%262%263%264%265%5C%5C%5B1ex%5D%0ADistance%20%28mi%29%2655%26110%26165%26220%26275%0A%5Cend%7Btabular%7D)
The rate at which she travels is given by

If Randy has driven for one more hour at the same rate, the number of hours she must have droven is 6 hrs and the total distance is given by
distance = 55 x 6 = 330 miles.
Answer: the distance of the base of the house to the foot of the ladder is 6.84 feet
Step-by-step explanation:
The scenario is shown in the attached photo.
Right angle triangle ABC is formed when the ladder leans against the wall of the house.
AC = the height of the ladder
AB = x feet = distance of the base of the house to the foot of the ladder
BC is the wall of the building.
To determine x, we will apply trigonometric ratio
Cos # = adjacent/hypotenuse
Where
# = 70 degrees
Hypotenuse = 20
Adjacent = x
Cos 70 = x/20
x = 20cos70
x = 20 × 0.3420
x = 6.84 feets