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21 votes
21 votes
Solve the system of equations graphically. Then classify

the system as consistent or inconsistent and the
equations as dependent or independent.
5x - y = 7
5x+6y= -7

Solve the system of equations graphically. Then classify the system as consistent-example-1
User PJx
by
2.6k points

1 Answer

24 votes
24 votes

Answer:

They are consistent and independent

Explanation:

Consistency

If two lines have an intersection point, they are said to be consistent. For example, two parallel lines do not have an intersection and therefore they are inconsistent.

In the problem, the two lines intersect at (1, -2) so they have a unique solution and therefore consistent.

Dependency

Two lines are said to be independent if one of them cannot be written as an integer multiple of the other. Or, in other words, if the slope-intercept form of both equations have different slope and y intercept

Note: slope-intercept form of an equation is y = mx + c where m is the slope and c the y intercept

Line 1: 5x - y = 7 can be written as y = 5x - 7 which has slope +5 and y intercept -7

Line2 : 5x + 6y = -7 can be re-written as y = (-5/6)x - (7/6). This has slope -5/6 and y intercept -7/6

Since slope and intercepts of both lines are different they form a system of independent equations


Solve the system of equations graphically. Then classify the system as consistent-example-1
User Ron Norris
by
2.6k points