Math  /  Geometry

QuestionFind the value of xx and yy for each figure below.

Studdy Solution
Now we have a system of equations from both triangles:
1. 5x+y=85 5x + y = 85
2. 3x+8y=109 3x + 8y = 109

Solve this system using substitution or elimination. Let's use substitution:
From equation 1, express yy in terms of xx:
y=855x y = 85 - 5x
Substitute yy in equation 2:
3x+8(855x)=109 3x + 8(85 - 5x) = 109 3x+68040x=109 3x + 680 - 40x = 109 37x+680=109 -37x + 680 = 109 37x=109680 -37x = 109 - 680 37x=571 -37x = -571 x=57137 x = \frac{571}{37} x=15.4324 x = 15.4324 (rounded to four decimal places)
Substitute xx back into the expression for yy:
y=855(15.4324) y = 85 - 5(15.4324) y=8577.162 y = 85 - 77.162 y=7.838 y = 7.838 (rounded to three decimal places)
The values of xx and yy are approximately:
x15.4324 x \approx 15.4324 y7.838 y \approx 7.838

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