Question

Find the values of the variables for which each statement is true, if possible.
$[\begin{matrix} 0 & 5 & x \\ - 1 & 3 & y + 2 \\ 4 & 1 & z \end{matrix}] = [\begin{matrix} 0 & w & 6 \\ - 1 & 3 & 0 \\ 4 & 1 & 8 \end{matrix}]$

Accepted Answer

First, carefully read the problem statement to identify the variables involved and the equations or expressions given. Since the problem references Examples 1 and 2, review those examples to understand the type of equations or statements you are dealing with. Write down the given equations or statements clearly. For example, if you have an equation like $$a = b$$, or an expression involving variables, write it in proper algebraic form. Determine what it means for the statement to be true. This usually involves solving the equation or system of equations for the variables. Set up the equation(s) accordingly. Use algebraic methods such as isolating variables, factoring, or applying inverse operations to solve for the variables. For example, if you have an equation like $$2x + 3 = 7$$, subtract 3 from both sides and then divide by 2 to isolate $$x. $$Check your solutions by substituting them back into the original statements to verify if they make the statements true. If no solution satisfies the statement, conclude that no such values exist.

Find the values of the variables for which each statement is true, if possible.
$[\begin{matrix} 0 & 5 & x \\ - 1 & 3 & y + 2 \\ 4 & 1 & z \end{matrix}] = [\begin{matrix} 0 & w & 6 \\ - 1 & 3 & 0 \\ 4 & 1 & 8 \end{matrix}]$

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Key Concepts

Solving Equations

Checking for Solutions

Understanding Variable Constraints