Math Problem Statement
solve it in normal way not augmented matrix
Solution
To solve the system of equations without using an augmented matrix, let's rewrite and solve it step-by-step. The given system is:
x_2 + 4x_3 = -5 \\ x_1 + 3x_2 + 5x_3 = -2 \\ 3x_1 + 7x_2 + 7x_3 = 6 \end{cases}$$ ### Step 1: Solve for $$x_2$$ in terms of $$x_3$$ from the first equation From the first equation: $$x_2 + 4x_3 = -5$$ $$x_2 = -5 - 4x_3$$ ### Step 2: Substitute $$x_2 = -5 - 4x_3$$ into the second and third equations Substitute into the second equation: $$x_1 + 3(-5 - 4x_3) + 5x_3 = -2$$ Simplify: $$x_1 - 15 - 12x_3 + 5x_3 = -2$$ $$x_1 - 15 - 7x_3 = -2$$ $$x_1 = 13 + 7x_3$$ Now, substitute $$x_2 = -5 - 4x_3$$ into the third equation: $$3x_1 + 7(-5 - 4x_3) + 7x_3 = 6$$ Simplify: $$3x_1 - 35 - 28x_3 + 7x_3 = 6$$ $$3x_1 - 35 - 21x_3 = 6$$ $$3x_1 = 41 + 21x_3$$ Substitute \( x_1 = 13 + 7x_3Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
System of Equations
Substitution Method
Formulas
Substitution method for solving linear systems
Theorems
Basic rules of algebra for solving systems of equations
Suitable Grade Level
College-level Linear Algebra or High School Advanced Algebra
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