High School

Solving Linear Systems:

Solve the system:

\[ x_1 + 4x_3 + 4x_4 = -9 \]

\[ x_2 - 4x_3 - 2x_4 = -3 \]

\[ 3x_1 - 2x_2 + 23x_3 + 16x_4 = -15 \]

\[ -x_2 + 4x_3 + 7x_4 = -17 \]

Find the values of:

a. \( x_1 = \)

b. \( x_2 = \)

c. \( x_3 = \)

d. \( x_4 = \)

Answer :

Explanation of how to solve a system of linear equations with step-by-step elimination method for x1, x2, x3, and x4.

Solution:

We first eliminate x1 from the equations, then x2, x3, and finally x4, leaving a single equation in one unknown.

By following the elimination method, we arrive at x1 = 3, x2 = -7, x3 = -2, and x4 = 1 as the solution to the system.

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