Answer:
x = -6.5 y= 3.75
Explanation:
Add angle 1 and 2 since they are both alternate interior angles
6x + y - 4 = x - 9y + 1
- x + 9y - x + 9y Subtract x and add 9y to both sides
5x + 10y - 4 = 1
+ 4 + 4 Add 4 to both sides
5x + 10y = 5
-5x - 5x Subtract 5x from both sides
10y = -5x + 5 Divide both sides by 10 to solve for y
y = -1/2x + 1/2
Use this equation to solve for x in the original equations
6x + (1/2x + 1/2) -4 = x - 9(-1/2x +1) - 1
6.5x - 3.5 = x + 4.5x - 9 - 1 Solve in the parentheses
6.5x - 3.5 = 5.5x - 10 Solve the right side of the equation
+ 3.5 + 3.5 Add 3.5 to both sides
6.5x = 5.5x - 6.5
- 5.5x - 5.5x Subtract 5.5x from both sides
x = -6.5
Use the new value of x to solve for y
6(-6.5) + y -4 = -6.5 -9y + 1
-43 + y = -5.5 -9y Simplify both sides
+43 + 43 Add 43 to both sides
y = 37.5 - 9y
+ 9y + 9y Add 9y to both sides
10y = 37.5
y = 3.75