graph each system?

Question

tell wheter the system has no solution, one solution, or infinely many solutions.

y= -4x+3
y=3x+2


please help, i don't understand

Answer 1

Replace "y" in first statement with second statemen's right hand side.

So you'll get

3x + 2 = -4X + 3
7x = -1
x = -1/7

Now find Y => 2 + 3 (-1/7)
Y = 11/7

This has only one soulution.

To clear things out in future lets look at some of the points.

One soulution means the set of equations have one & only one solution where all the veriables satify that answer. In other words these lines in co-ordinate plane intesects at one point only.
Ex - your question.


No solutions mean The line have no intersections. Consider a railway line. Do they intersect at any place ?? Parrelal lines have no solutions.
Ex : y = 3x + 8
y = 3x + 1
These line are parrelal & have no solution.

Infintely many solutions mean They lines or curves in the co-ordinates system intersect at every point or it has infinite intersection points.
Ex : y = 3x + 2
2y = 6x + 4
(these two lines are the same. So they intersect at ever point meaning they have infintely many solutions)

Hope this helps...

Cheers,
Codered

Answer 2

y = - 4x + 3- - - - - - -Equation 1
y = 3x + 2- - - - - - - -Equation 2
- - - - - - - - - -

Convert equation 2 to standard form

y = 3x + 2

- 3x + y = 3x + 2 - 3x

- 3x + y = 2. . . .Standard form

- - - - - - - - - -

Insert the y value equation 1 into standard form equation

- 3x + y = 2

- 3x + (- 4x + 3 = 2

- 3x - 4x + 3 = 2

- 7x + 3 = 3

- 7x + 3 - 3 = 2 - 3

- 7x = - 1

- 7x / - 7 = - 1 / - 7

x = - 1 / - 7

x = 1/7

Insert the x value into equation 1

y = - 4x + 3

y = - 4(1/7) + 3

y = - 4/7 + 3

y = - 4/7 + 21/7

y = 17/7

Insert the y value into equation 1

- - - - - - - - - - - - - - - - - - - - - - - - -
Check for equation 1

y = - 4x + 3

17/7 = - 4(1/7) + 3

17/7 = - 4/7 + 3

17/7 = - 4/7 + 21 / 7

17/7 = 17/7

- - - - - - - - - -

Check for equation 2

y = 3x + 2

17/7 = 3(1/7) + 2

17/7 = 3/7 + 2

17/7 = 3/7 + 14/7

17/7 = 17/7

- - - - - - - - - - - -

Both equations balance

The solution set is { 1/7 , 17/7 }

- - - - - - - s-

Answer 3

one solution because one of the linear is positive slope and the other is negative slope. And they intersect at only one point. For two points, one of the equations have to be a quadratic. And for infinite the equations are equal. No solutions is when the slopes are the same.

Answer 4

first one is 3/4
second one is -2/3

Aka its asking you to find out how many times the graph will pass the x-axis, since these are linear graphs it will only pass through once.

Answer 5

where the lines intersect i think is the answer