Question

PLEASE HELP ME WITH THIS I WILL MARK BRAINLIEST!! Classify each system of equations as having a single solution, no solution, or infinite solutions.

Answer 1

Answer:

see the explanation

see the attached figure

Step-by-step explanation:

Part 1) we have

$y=11-2x$ ----> equation A

$4x-y=7$

Isolate the variable y

$y=4x-7$ ----> 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

$x=12-3y$

isolate the variable y

$y=-(1/3)x+4$ -----> equation A

$3x+9y=24$

isolate the variable y

$y=-(1/3)x+(8/3)$  ----> 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

$2x+y=7$

isolate the variable y

$y=-2x+7$ -----> equation A

$-6x=3y-21$

isolate the variable y

$y=-2x+7$  ----> 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

$x+y=15$

isolate the variable y

$y=-x+15$ -----> equation A

$2x-y=15$

isolate the variable y

$y=2x-15$  ----> 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

$2x+y=7$

isolate the variable y

$y=-2x+7$ -----> equation A

$-4x=2y+14$

isolate the variable y

$y=2x-7$  ----> 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

$x+4y=6$

isolate the variable y

$y=-0.25x+1.5$ -----> equation A

$2x=12-8y$

isolate the variable y

$y=-0.25x-1.5$  ----> 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