What are two equations that are in standard form and equivalent to 6x+2y=8?

The two equations that are equivalent to given equation 6x + 2y = 8 are 3x + y = 4 and 12x + 4y = 16

Solution:

Given that we have to write two equations in standard form that is equivalent to 6x + 2y = 8

The standard form of an equation is Ax + By = C. In this kind of equation, x and y are variables and A, B, and C are integers

Given equation is:

6x + 2y = 8

Taking 2 as common term,

2(3x + y) = 8

3x + y = 4

Thus the above equation 3x + y = 4 is equivalent to given equation

Any equation that is a multiple of given equation 6x + 2y = 8 would be equivalent.

Multiply 6x + 2y = 8 by 2

[ note that you can multiply by any term like 0.5, 3, 3.5 and so on. Here we choose 2 to multiply ]

2(6x + 2y = 8) ⇒ 12x + 4y = 16

Thus the two equations that are equivalent to given equation are 3x + y = 4 and 12x + 4y = 16

b

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)