Answer: x = 15, y = 6
Explanation:
1). (7y - 1) + (9x + 4) = 180 (the are supplementary angles)
2). (4x-7) + (7y - 1) + 86 = 180 (sum of angles in a triangle)
7y - 1 + 9x + 4 = 180
7y + 9x + 3 = 180
9x + 7y = 177
4x - 7 + 7y - 1 + 86 = 180
4x + 7y - 8 + 86 = 180
4x + 7y + 78 = 180
4x + 7y = 102
Now solve the system of equations
subtract the two equations
9x + 7y = 177
-(4x + 7y) = -(102)
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5x = 75
x = 15
Substitute the value of x into either equation to find y
4(15) + 7y = 102
60 + 7y = 102
7y = 42
y = 6