SOLUTION: Solve the system by graphing. 3x-2y=4 -6x+4y=7

Question 158543: Solve the system by graphing.
3x-2y=4
-6x+4y=7
Found 2 solutions by gonzo, Electrified_Levi:
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
solving the equation by algebraic means, we get

solving for y in the first equation, we get

substituting this for y in the second equation, we get

this becomes

since the x cancels out we are left with
-8=7
which means there is no solution.
looking at both equations in y = slope intercept form, we see

and

general form of the slope intercept form of the equation is y=m*x+b
where m is the slope and b is the y intercept when x = 0.
slope of the first equation is 3/2
slope of the second equation is 6/4 which simplifies to 3/2.
slopes are equal so lines are parallel.
solving by equation below shows that right away.

Answer by Electrified_Levi(103) (Show Source): You can put this solution on YOUR website!
Hi, Hope I can help
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Solve the system by graphing.

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Points are given as (x,y), to find points on both of these lines, you just replace "x" with any number and solve for "y"
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Lets find some points on the first line
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, (we can use any number for "x", then we solve for "y"
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Lets replace "x" with "2", = =
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We will move (-2y) over to the right side
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= = , we will move "4" to the left side
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= = =
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To get "y", we will divide each side by "2"
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= = ,
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"x" = 2
"y" = 1
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Since points are given as (x,y), this point would be (2,1)
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(2,1) is a point of the line(We can check by replacing "x" with "2", "y" with "1", = = = (True)
.

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Lets find another point,
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Lets replace "x" with "0"
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= = =
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We can multiply each side by (-1) to get (-2y) positive
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= = , to find "y" we will divide each side by "2"
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= =
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"x" = 0
"y" = (-2)
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Another point on the line is (0,-2)(x,y)(we can check by replacing "x" with "0", "y" with (-2), = = = (True)
.

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Another point on the line is (-4,-8), We can check by replacing "x" with (-4), "y" with (-8), = = = (True)
.

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Lets draw a line through the points,
.

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Now lets find some points for the second equation,
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Lets replace "x" with , = =
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"4y" has to equal "4", so , divide each side by "4", = =
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x =
y = 1
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One point on the line is (,1 )(We can check by replacing "x" with ,"y" with "1", = = = (True)
.

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Replace "x" with "4", = =
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"4y" will have to equal "31", , dividing each side by "4" will get "y"
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= =
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x = 4
y = , or 7
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The point is (4,), (we can check by replacing "x" with "4", "y" with , = = = (True)
.

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Another point on the line is ( 0, ), ( we can check by replacing "x" with "0", "y" with "", = = = (True)
.

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Lets draw a line through the points
.

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These lines are parallel, they don't have any points that intersect each other, there is no solution to the system of equations
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Hope I helped, Levi
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