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Sagot :
Answer:
Part 1) we have
----> equation A
Isolate the variable y
----> 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
isolate the variable y
-----> equation A
isolate the variable y
----> 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
isolate the variable y
-----> equation A
isolate the variable y
----> 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
isolate the variable y
-----> equation A
isolate the variable y
----> 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
isolate the variable y
-----> equation A
isolate the variable y
----> 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
isolate the variable y
-----> equation A
isolate the variable y
----> 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
Step-by-step explanation:
Answer:
Starting with the first one, we need to convert both of the equations into slope-intercept form. y = -2x + 5 is already in that form, now we just need to do it to 4x + 2y = 10.
2y = -4x + 10
y = -2x +5
Since both equations give the same line, the first one has infinite solutions.
Now onto the second one. Once again, the first step is to convert both of the equations into slope-intercept form.
x = 26 - 3y becomes
3y = -x + 26
y = -1/3x + 26/3
2x + 6y = 22 becomes
6y = -2x + 22
y = -1/3 x + 22/6
Since the slopes of these two lines are the same, that means that they are parallel, meaning that this one has no solutions.
Now the third one. We do the same steps.
5x + 4y = 6 becomes
4y = -5x + 6
y = -5/4x + 1.5
10x - 2y = 7 becomes
2y = 10x - 7
y = 5x - 3.5
Since these two equations are completely different, that means that this system has one solution.
Now the fourth one. We do the same steps again.
x + 2y = 3 becomes
2y = -x + 3
y = -0.5x + 1.5
4x + 8y = 15 becomes
8y = -4x + 15
y = -1/2x + 15/8
Once again, since these two lines have the same slopes, that means that they are parallel, meaning that this one has no solutions.
Now the fifth one.
3x + 4y = 17 becomes
4y = -3x + 17
y = -3/4x + 17/4
-6x = 10y - 39 becomes
10y = -6x + 39
y = -3/5x + 3.9
Since these equations are completely different, there is a single solution.
Last one!
x + 5y = 24 becomes
5y = -x + 24
y = -1/5x + 24/5
5x = 12 - y becomes
y = -5x +12
Since these equations are completely different, this system has a single solution.
Step-by-step explanation:
hope this helps you out:)
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