QQuestionMathematics
QuestionMathematics
"Solve the system of equations by any method.
3x−4y+ 2z =−15 (1)
2x+ 4y+z = 16 (2)
2x+ 3y+ 5z = 20 (3)
Enter the exact answer as an ordered triple, (x,y,z)."
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Answer
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Step 1: Let's use the substitution method to solve this system of equations.
z = 16 - 2x - 4y \quad (4)
First, we'll solve equation (2) for z:
Step 2: Now, we'll substitute equation (4) into equations (1) and (3) to eliminate the variable z:
3x - 4y + 2(16 - 2x - 4y) = -15
For equation (1):
Final Answer
The solution to the system of equations is approximately (x, y, z) = \left(- 102.86, -\frac{205}{7}, 315.14\right).
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