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Solve the following system of linear equations: $\newline$ $x_1+x_2+x_3=2$ $\newline$ $2x_1-x_2+x_3=9$ $\newline$ $2x_1+3x_2+4x_3=4$ $\newline$ Determine the values of $x_1, x_2, x_3$ .

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Choose two-step equations: word problems

Full solution

Q. Solve the following system of linear equations:

\newline

x_1+x_2+x_3=2

\newline

2x_1-x_2+x_3=9

\newline

2x_1+3x_2+4x_3=4

\newline

Determine the values of

x_1, x_2, x_3

.

Write Equations: Step $1$ : Write down the system of equations. $\newline$ Equations given: $\newline$ $1$ . $x_1 + x_2 + x_3 = 2$ $\newline$ $2$ . $2x_1 - x_2 + x_3 = 9$ $\newline$ $3$ . $2x_1 + 3x_2 + 4x_3 = 4$
Use Elimination: Step $2$ : Use elimination to simplify the equations. $\newline$ Eliminate $x_3$ from equations $1$ and $2$ : $\newline$ Add equation $1$ and $2$ : $\newline$ $x_1 + x_2 + x_3 + 2x_1 - x_2 + x_3 = 2 + 9$ $\newline$ $3x_1 + 2x_3 = 11$
Substitute and Solve: Step $3$ : Substitute $3x_1 + 2x_3 = 11$ into equation $3$ . $\newline$ Replace $3x_1 + 2x_3$ in equation $3$ : $\newline$ $3x_1 + 2x_3 + 3x_2 + 4x_3 = 4$ $\newline$ $6x_2 + 6x_3 = -7$ (This is incorrect, should be $3x_2 + 2x_3 = -7$ )

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