Solve the system of equations algebraically.

*If necessary, write your answers as fractions in simplest form.

y = x + 2
y = -3x

Step-by-step explanation:

y = x + 2  (i)

y = -3x (ii)

substitute y = -3x i equation (i)

-3x = x + 2

-3x -x = 2

-4x = 2

x = 2/-4

x = -1/2

Substitute x = -1/2 in (ii)

y = -3 * -1/2

y = 3/2

1. perpendicular

2. parallel

3. perpendicular

< 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)