Answer:
see the explanation
see the attached figure
Step-by-step explanation:
Part 1) we have
[tex]y=11-2x[/tex] ----> equation A
[tex]4x-y=7[/tex]
Isolate the variable y
[tex]y=4x-7[/tex] ----> equation B
Compare the slope of both lines
The slopes are different
That means
The lines intersect at one point
therefore
The system has one solution
Part 2) we have
[tex]x=12-3y[/tex]
isolate the variable y
[tex]y=-(1/3)x+4[/tex] -----> equation A
[tex]3x+9y=24[/tex]
isolate the variable y
[tex]y=-(1/3)x+(8/3)[/tex] ----> equation B
Compare equation A and equation B
The slopes are equal
The y-intercept are different
That means
we have parallel lines with different y-intercept
so
The lines don't intersect
therefore
The system has no solution
Part 3) we have
[tex]2x+y=7[/tex]
isolate the variable y
[tex]y=-2x+7[/tex] -----> equation A
[tex]-6x=3y-21[/tex]
isolate the variable y
[tex]y=-2x+7[/tex] ----> equation B
Compare equation A and equation B
The equations are identical
That means
Is the same line
so
The system has infinitely solutions
Part 4) we have
[tex]x+y=15[/tex]
isolate the variable y
[tex]y=-x+15[/tex] -----> equation A
[tex]2x-y=15[/tex]
isolate the variable y
[tex]y=2x-15[/tex] ----> equation B
Compare the slope of both lines
The slopes are different
That means
The lines intersect at one point
therefore
The system has one solution
Part 5) we have
[tex]2x+y=7[/tex]
isolate the variable y
[tex]y=-2x+7[/tex] -----> equation A
[tex]-4x=2y+14[/tex]
isolate the variable y
[tex]y=2x-7[/tex] ----> equation B
Compare the slope of both lines
The slopes are different
That means
The lines intersect at one point
therefore
The system has one solution
Part 6) we have
[tex]x+4y=6[/tex]
isolate the variable y
[tex]y=-0.25x+1.5[/tex] -----> equation A
[tex]2x=12-8y[/tex]
isolate the variable y
[tex]y=-0.25x-1.5[/tex] ----> equation B
Compare equation A and equation B
The slopes are equal
The y-intercept are different
That means
we have parallel lines with different y-intercept
so
The lines don't intersect
therefore
The system has no solution
