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

Question

The options are; (0,2) (-4,0), (-4, -2) (0, -2)

Answer 1

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.

 

 

Answer 2

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.

 

 

Answer 3

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.