To solve for x and y, we can use the properties of corresponding angles formed by a transversal line intersecting two parallel lines. Specifically, corresponding angles are congruent, so we can set up the following equations:
(6x + 11)° = (3y + 8)°
(10x - 13)° = (3y + 8)°
Subtracting (3y + 8)° from both sides of the first equation, we get:
6x + 11 - 3y - 8 = 0
6x - 3y - 3 = 0
Subtracting (3y + 8)° from both sides of the second equation, we get:
10x - 13 - 3y - 8 = 0
10x - 3y - 21 = 0
We can solve the system of equations using elimination or substitution.
Using elimination, we can add the two equations to get:
(6x - 3y - 3) + (10x - 3y - 21) = 0
16x - 6y - 24 = 0
Dividing both sides by 6, we get:
x - y - 4 = 0
x = y + 4
Substituting this expression for x into the first equation, we get:
(y + 4) + 11 - 3y - 8 = 0
-2y - 3 = 0
y = 1.5
Substituting y = 1.5 into the expression for x, we get:
x = 1.5 + 4
x = 5.5
Therefore, x = 5.5 and y = 1.5.
Using substitution, we can solve the system of equations by solving one of the equations for one of the variables and substituting this expression into the other equation.
For example, we can solve the first equation for x:
x = (3y + 8 - 11) / 6
x = (3y - 3) / 6
Substituting this expression for x into the second equation, we get:
(10 * (3y - 3) / 6) - 13 - 3y - 8 = 0
(5y - 15) - 13 - 3y - 8 = 0
2y - 23 = 0
y = 11.5
Substituting y = 11.5 into the expression for x, we get:
x = (3 * 11.5 - 3) / 6
x = 5.5
Therefore, x = 5.5 and y = 11.5.
I hope this helps!