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Mathematics 8 Online
klmjnmkj:

math help

klmjnmkj:

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klmjnmkj:

@florisalreadytaken

dewayneeeeeee:

What is it

Florisalreadytaken:

were given this system: \[ \begin{cases} -2x+7y=-6\\-4x+14y=-12 \end{cases} \] first step is to make the 1st equation be ralatable to the 2nd one -- in our case, we will have to multiply by -2: \[ \begin{cases} ( -2x+7y=-6 ) \times (-2) \\ -4x+14y=-12 \end{cases} \] by adding it together we get: \[ (4x-14y=12) + (-4x+14y=-12) = 0 \] that tells us that this equation, intersects at an infinite number of points. lets solve for y (im going to use the 1st equation): \[ 4x-14y=12 \overset{\text{take 4x to the other side}}{======== \Rightarrow} -14y = 12 - 4x\] \[ \overset{\text{divide by -14 on both sides}}{========== \Rightarrow} \frac{-14 y}{-14}=\frac{12}{-14}+\frac{-4 x}{-14} \] \[ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \updownarrow \] \[ y=\frac{12}{-14}+\frac{-4 x}{-14} \] thus, \[ y=-\frac{6}{7}+\frac{2 x}{7} \] which can also be written as: \[ y= \frac{2 x}{7}-\frac{6}{7} \] that said, we get: \[ \left( x,-\frac{6}{7}+\frac{2 x}{7} \right) \] which option is that?

Florisalreadytaken:

i told you it would take long to explain : D

klmjnmkj:

c?

Florisalreadytaken:

no... the last one

VIBE:

@VIBE wrote:
"Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : -2*x+7*y-(-6)=0 Solve -2x+7y+6 = 0 Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK). "y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis. In this formula : y tells us how far up the line goes x tells us how far along m is the Slope or Gradient i.e. how steep the line is b is the Y-intercept i.e. where the line crosses the Y axis The X and Y intercepts and the Slope are called the line properties. We shall now graph the line -2x+7y+6 = 0 and calculate its properties Notice that when x = 0 the value of y is -6/7 so this line "cuts" the y axis at y=-0.85714 y-intercept = -6/7 = -0.85714 When y = 0 the value of x is 3/1 Our line therefore "cuts" the x axis at x= 3.00000 x-intercept = 6/2 = 3 Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -0.857 and for x=2.000, the value of y is -0.286. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.286 - (-0.857) = 0.571 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN) Slope = 0.571/2.000 = 0.286 1. Slope = 0.571/2.000 = 0.286 2. x-intercept = 6/2 = 3 3. y-intercept = -6/7 = -0.85714 That is the first answer." "The second answer is Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : Pull out like factors : -4x + 14y + 12 = -2 • (2x - 7y - 6) -4*x+14*y-(-12)=0 Solve : -2 = 0 This equation has no solution. A a non-zero constant never equals zero. Solve 2x-7y-6 = 0 Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK). "y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.In this formula : y tells us how far up the line goes x tells us how far along m is the Slope or Gradient i.e. how steep the line is b is the Y-intercept i.e. where the line crosses the Y axis The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2x-7y-6 = 0 and calculate its properties Notice that when x = 0 the value of y is 6/-7 so this line "cuts" the y axis at y=-0.85714 y-intercept = 6/-7 = -0.85714 When y = 0 the value of x is 3/1 Our line therefore "cuts" the x axis at x= 3.00000 x-intercept = 6/2 = 3 Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -0.857 and for x=2.000, the value of y is -0.286. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.286 - (-0.857) = 0.571 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN) Slope = 0.571/2.000 = 0.286 1. Slope = 0.571/2.000 = 0.286 3. x-intercept = 6/2 = 3 3. y-intercept = 6/-7 = -0.85714 that is your second answer"

Florisalreadytaken:

what?😹😹😹

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