Question

Solve the given system of equations.

{y=11x+20y=−2+11x

Answer 1

Answer:

11x - 20y = 28

3x + 4y = 36

multiply second equation by 5 (so when add two equations the y terms will cancel):

11x - 20y = 28

15x + 20y = 180

add two equations together:

26x = 208

x = 8

substitute 8 for x in equation 3x + 4y = 36 to solve for y:

3(8) + 4y = 36

24 + 4y = 36

4y = 12

y = 3

Explanation:

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Answer 2

Answer:

No solution (inconsistent system)

Explanation:

Solving the system

$y=11x+20\\y=-2+11x$

Since both equations already have the "y" isolated, substitution of the first equation into the second equation will probably be the easiest.

$11x+20=-2+11x$

$(11x+20)-11x=(-2+11x)-11x$

$20=-2$

Since 20 never equals -2 (never, not for any value of x or y), then there is no solution to this system of equations.  This system is classified as "inconsistent".

Alternative way to look at this problem

A different way of thinking about this problem would be to look at both equations in their slope intercept form:

$y=11x+20\\y=11x-2$

Since both equations have a slope of 11, the lines are parallel.  If their y-intercepts were the same, they would be parallel and overlapping.  However, since their y-intercepts are different, they are parallel and not overlapping.  Thus, they will never cross or touch each other.

Since a solution to a system of equations is visually where the lines cross or overlap, there is no solution to the system.