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
Still Need Help?
Join the QuestionCove community and study together with friends!
Sign Up
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"