Write the following linear systems as augmented matrices. The first system is $$3x + 8y = -3$$ and $$2x = -5y - 3$$. The second system is $$2x - 5y + 3z = 8$$, $$3x - y + 4z = 7$$, and $$x + 3y + 2z = -3$$. Before extracting the numbers, ensure every equation is in standard form. For example, rewrite the second equation of the two-variable system as $$2x + 5y = -3$$ so the variables are correctly aligned.

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To write a system of linear equations as an augmented matrix, first ensure each equation is in standard form. For example, in the two-variable system $$5x - 3y = -1$$ and $$y = 2x - 2$$, the second equation must be rewritten as $$-2x + y = -2$$ before extracting the coefficients and constants to form the matrix rows. For a three-variable system already in standard form, such as $$6x - 5y + 2z = 3$$, $$2x + y - 4z = 5$$, and $$3x - 3y + z = -1$$, the numerical values can be directly mapped to the matrix rows, with a vertical line replacing the equal signs.

Writing a System of Linear Equations as an Augmented Matrix

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Practice: Formulating an Augmented Matrix from a Two-Variable and Three-Variable System

Construct an augmented matrix for the following linear systems. The first system is $$11x = -9y - 5$$ and $$7x + 5y = -1$$. The second system is $$5x - 3y + 2z = -5$$, $$2x - y - z = 4$$, and $$3x - 2y + 2z = -7$$. First, rewrite any non-standard equations, such as changing $$11x = -9y - 5$$ to $$11x + 9y = -5$$. Then, extract the coefficients and constants row by row, using a vertical line to represent the equal signs.

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