Answer:
x = 12 , y = 16
Explanation:
Assuming the figure to be a parallelogram
In a parallelogram
• opposite angles are congruent (equal ), then
6x + 3y - 8 = 7y ( subtract 7y from both sides )
6x - 4y - 8 = 0 ( add 8 to both sides )
6x - 4y = 8 → (1)
In a parallelogram
• consecutive angles are supplementary ( sum to 180 ) , then
4x + 20 + 7y = 180 ( subtract 20 from both sides )
4x + 7y = 160 → (2)
Now we can solve the 2 equations, simultaneously
6x - 4y 8 → (1)
4x + 7y = 160 → (2)
multiplying (1) by 7 and (2) by 4 and adding the result will eliminate y
42x - 28y = 56 → (3)
16x + 28y = 640 → (4)
add (3) and (4) term by term to eliminate y
(42x + 16x ) + (- 28y + 28y ) = 56 + 640
58x + 0 = 696
58x = 696 ( divide both sides by 58 )
x = 12
substitute x = 12 into either of the 2 original equations and solve for y
substituting into (2)
4(12) + 7y = 160
48 + 7y = 160 ( subtract 48 from both sides )
7y = 112 ( divide both sides by 7 )
y = 16
the values are x = 12 and y = 16