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Determine which of the ordered pairs is a solution for the equation 2x – 4y = 8.

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3 Answers

Hi Adeline;
2x – 4y = 8
(0,2) (-4,0), (-4, -2) (0, -2)
 
(0,2) and (0,-2) are y-intercepts, the value of y when x=0.
The equation is currently in standard form...
Ax+By=C, A>0
Let's convert the equation into slope-intercept form..
y=mx+b
m is the slope.
b is the y-intercept.
2x-4y=8
Let's subtract 2x from both sides...
2x-2x-4y=-2x+8
-4y=-2x+8
Let's divide both sides by -4...
(-4y)/-4=(-2x+8)/-4
y=(1/2)x-2
y-intercept is -2, (0,-2)
We have ruled-in one answer (0,-2), and ruled-out the other (0,2).
 
(-4,0) is the x-intercept, the value of x when y=0.
Let's return to the original equation and plug-in y=0...
2x – 4y = 8
2x-[(4)(0)]=8
2x=8
x=4
This is the wrong result.  We have ruled-out another answer, (-4,0).
 
(-4,-2)
This one has no special features.  We will have to plug it into the equation...
2x-4y=8
[(2)(-4)]-[(4)(-2)]=8
-8-(-8)=8
Subtracting a negative number is the same as adding a positive number...
-8+8=8
Does not work.
 
 
Hi Adeline,
 
2x-4y=8
 
left hand side =L.H.S and right hand side = R.H.S
 
If L.H.S=R.H.S, then the given ordered pair is the solution of the equation. 
 
1)  (0,2)
 
L.H.S=2(0)-4(2)=0-8=-8≠8=R.H.S
 
(0,2) is not the solution.
 
2)  (-4,0)
 
L.H.S=2(-4)-4(0)=-8-0=-8≠8=R.H.S
 
(-4,0) is not the solution.
 
3)  (-4,-2)
 
L.H.S=2(-4)-4(-2)=-8+8=0≠8=R.H.S
 
(-4,-2) is not the solution.
 
4) (0,-2)
 
L.H.S=2(0)-4(-2)=0+8=8=R.H.S
 
(0,-2) is the solution.
 
 
2X - 4Y = 8
 
 
( 0,2)
 
a.
2(0) - 4 ( 2 ) = -8
 
   No
 
b.
     ( - 4, 0 )
 
 2 ( -4 ) - 4 ( 0 ) = -8
 
    No
c.
( - 4 , -2 )
 
 2( -4 ) - 4 ( - 2) = 0
 
    No.
 
d.
    ( 0 , - 2)
 
   2 ( 0 ) - 4 ( -2 ) =0 +8 = 8
 
  Yes
       The correct answer is d.