Question

solve for x and y.
equation:
x=
equation:
y=

Explanation:

Step1: Set up equation for x

Since $6x + 11$ and $8x-13$ are vertical - angles and vertical - angles are equal, we set up the equation $6x + 11=8x - 13$.
$6x+11 = 8x - 13$

Step2: Solve for x

Subtract $6x$ from both sides:
$11=8x - 6x-13$
$11 = 2x-13$
Add 13 to both sides:
$11 + 13=2x$
$24 = 2x$
Divide both sides by 2:
$x = 12$

Step3: Set up equation for y

Assume the angle $5y + 2$ is supplementary to either $6x + 11$ or $8x - 13$. Let's use the fact that linear - pair of angles are supplementary. If we consider the linear - pair relationship, and since $x = 12$, then $6x+11=6\times12 + 11=72 + 11 = 83$.
The equation for y is $5y+2+83 = 180$ (because the sum of angles in a linear - pair is 180 degrees).
$5y+85 = 180$

Step4: Solve for y

Subtract 85 from both sides:
$5y=180 - 85$
$5y = 95$
Divide both sides by 5:
$y = 19$

Answer:

Equation for x: $6x + 11=8x - 13$
$x = 12$
Equation for y: $5y+2+(6x + 11)=180$ (with $x = 12$), or $5y+2 + 83=180$
$y = 19$